This document discusses methods for summarizing Lego-like sphere and torus maps. It begins by introducing the concept of ({a,b},k)-maps, which are k-valent maps with faces of size a or b. It then discusses several challenges in enumerating and drawing such maps, including enumerating all possible Lego decompositions. Specific enumeration methods are described, such as using exact covering problems or satisfiability problems. The document also discusses challenges in graph drawing representations, and suggests using primal-dual circle packings as a promising approach.
Enumeration methods are very important in a variety of settings, both mathematical and applications. For many problems there is actually no real hope to do the enumeration in reasonable time since the number of solutions is so big. This talk is about how to compute at the limit.
The talk is decomposed into:
(a) Regular enumeration procedure where one uses computerized case distinction.
(b) Use of symmetry groups for isomorphism checks.
(c) The augmentation scheme that allows to enumerate object up to isomorphism without keeping the full list in memory.
(d) The homomorphism principle that allows to map a complex problem to a simpler one.
THE RESULT FOR THE GRUNDY NUMBER ON P4- CLASSESgraphhoc
Our work becomes integrated into the general problem of the stability of the network ad hoc. Some, works
attacked (affected) this problem. Among these works, we find the modelling of the network ad hoc in the
form of a graph. We can resume the problem of coherence of the network ad hoc of a problem of allocation
of frequency
We study a new class of graphs, the fat-extended P4 graphs, and we give a polynomial time algorithm to
calculate the Grundy number of the graphs in this class. This result implies that the Grundy number can be
found in polynomial time for many graphs
In [8] Liang and Bai have shown that the - 4 kC snake graph is an odd harmonious graph for each k ³ 1.
In this paper we generalize this result on cycles by showing that the - n kC snake with string 1,1,…,1 when
n º 0 (mod 4) are odd harmonious graph. Also we show that the - 4 kC snake with m-pendant edges for
each k,m ³ 1 , (for linear case and for general case). Moreover, we show that, all subdivision of 2 k mD -
snake are odd harmonious for each k,m ³ 1 . Finally we present some examples to illustrate the proposed
theories.
In this talk, we give an overview of results on numerical integration in Hermite spaces. These spaces contain functions defined on $\mathbb{R}^d$, and can be characterized by the decay of their Hermite coefficients. We consider the case of exponentially as well as polynomially decaying Hermite coefficients. For numerical integration, we either use Gauss-Hermite quadrature rules or algorithms based on quasi-Monte Carlo rules. We present upper and lower error bounds for these algorithms, and discuss their dependence on the dimension $d$. Furthermore, we comment on open problems for future research.
Enumeration methods are very important in a variety of settings, both mathematical and applications. For many problems there is actually no real hope to do the enumeration in reasonable time since the number of solutions is so big. This talk is about how to compute at the limit.
The talk is decomposed into:
(a) Regular enumeration procedure where one uses computerized case distinction.
(b) Use of symmetry groups for isomorphism checks.
(c) The augmentation scheme that allows to enumerate object up to isomorphism without keeping the full list in memory.
(d) The homomorphism principle that allows to map a complex problem to a simpler one.
THE RESULT FOR THE GRUNDY NUMBER ON P4- CLASSESgraphhoc
Our work becomes integrated into the general problem of the stability of the network ad hoc. Some, works
attacked (affected) this problem. Among these works, we find the modelling of the network ad hoc in the
form of a graph. We can resume the problem of coherence of the network ad hoc of a problem of allocation
of frequency
We study a new class of graphs, the fat-extended P4 graphs, and we give a polynomial time algorithm to
calculate the Grundy number of the graphs in this class. This result implies that the Grundy number can be
found in polynomial time for many graphs
In [8] Liang and Bai have shown that the - 4 kC snake graph is an odd harmonious graph for each k ³ 1.
In this paper we generalize this result on cycles by showing that the - n kC snake with string 1,1,…,1 when
n º 0 (mod 4) are odd harmonious graph. Also we show that the - 4 kC snake with m-pendant edges for
each k,m ³ 1 , (for linear case and for general case). Moreover, we show that, all subdivision of 2 k mD -
snake are odd harmonious for each k,m ³ 1 . Finally we present some examples to illustrate the proposed
theories.
In this talk, we give an overview of results on numerical integration in Hermite spaces. These spaces contain functions defined on $\mathbb{R}^d$, and can be characterized by the decay of their Hermite coefficients. We consider the case of exponentially as well as polynomially decaying Hermite coefficients. For numerical integration, we either use Gauss-Hermite quadrature rules or algorithms based on quasi-Monte Carlo rules. We present upper and lower error bounds for these algorithms, and discuss their dependence on the dimension $d$. Furthermore, we comment on open problems for future research.
This is a detailed review of ACM International Collegiate Programming Contest (ICPC) Northeastern European Regional Contest (NEERC) 2016 Problems. It includes a summary of problem and names of problem authors and detailed runs statistics for each problem.
Problem statements are available here:
http://neerc.ifmo.ru/information/problems.pdf
The beginning of the following video has the actual review (in Russian): https://www.youtube.com/watch?v=fN25KkNYsjA
This is a detailed review of ACM International Collegiate Programming Contest (ICPC) Northeastern European Regional Contest (NEERC) 2015 Problems. It includes a summary of problem and names of problem authors and detailed runs statistics for each problem. Video of the actual presentation that was recorded during NEERC is here https://www.youtube.com/watch?v=vn7v1MuWXdU (in Russian)
Note: there were only preliminary stats avaialble, because problems review was happening before before the closing ceremony. This published presentation has full stats.
In this paper, we introduce the notions of m-shadow graphs and n-splitting graphs,m ³ 2, n ³ 1. We
prove that, the m-shadow graphs for paths, complete bipartite graphs and symmetric product between
paths and null graphs are odd graceful. In addition, we show that, the m-splitting graphs for paths, stars
and symmetric product between paths and null graphs are odd graceful. Finally, we present some examples
to illustrate the proposed theories.
We study QPT (quasi-polynomial tractability) in the worst case setting of linear tensor product problems defined over Hilbert spaces. We prove QPT for algorithms that use only function values under three assumptions'
1. the minimal errors for the univariate case decay polynomially fast to zero,
2. the largest singular value for the univariate case is simple,
3. the eigenfunction corresponding to the largest singular value is a multiple of the function value at some point.
The first two assumptions are necessary for QPT. The third assumption is necessary for QPT for some Hilbert spaces.
Joint work with Erich Novak
In [1] Abdel-Aal has introduced the notions of m-shadow graphs and n-splitting graphs, for all m, n ³ 1.
In this paper, we prove that, the m-shadow graphs for paths and complete bipartite graphs are odd
harmonious graphs for allm³ 1. Also, we prove the n-splitting graphs for paths, stars and symmetric
product between paths and null graphs are odd harmonious graphs for all n³ 1. In addition, we present
some examples to illustrate the proposed theories. Moreover, we show that some families of graphs admit
odd harmonious libeling.
In this paper, we show that the number of edges for any odd harmonious Eulerian graph is congruent to 0 or 2 (mod 4), and we found a counter example for the inverse of this statement is not true. We also proved that, the graphs which are constructed by two copies of even cycle Cn sharing a common edge are odd harmonious. In addition, we obtained an odd harmonious labeling for the graphs which are constructed by two copies of cycle Cn sharing a common vertex when n is congruent to 0 (mod 4). Moreover, we show that, the Cartesian product of cycle graph Cm and path Pn for each n ≥ 2, m ≡ 0 (mod 4) are odd harmonious graphs. Finally many new families of odd harmonious graphs are introduced.
This is a detailed review of ACM International Collegiate Programming Contest (ICPC) Northeastern European Regional Contest (NEERC) 2016 Problems. It includes a summary of problem and names of problem authors and detailed runs statistics for each problem.
Problem statements are available here:
http://neerc.ifmo.ru/information/problems.pdf
The beginning of the following video has the actual review (in Russian): https://www.youtube.com/watch?v=fN25KkNYsjA
This is a detailed review of ACM International Collegiate Programming Contest (ICPC) Northeastern European Regional Contest (NEERC) 2015 Problems. It includes a summary of problem and names of problem authors and detailed runs statistics for each problem. Video of the actual presentation that was recorded during NEERC is here https://www.youtube.com/watch?v=vn7v1MuWXdU (in Russian)
Note: there were only preliminary stats avaialble, because problems review was happening before before the closing ceremony. This published presentation has full stats.
In this paper, we introduce the notions of m-shadow graphs and n-splitting graphs,m ³ 2, n ³ 1. We
prove that, the m-shadow graphs for paths, complete bipartite graphs and symmetric product between
paths and null graphs are odd graceful. In addition, we show that, the m-splitting graphs for paths, stars
and symmetric product between paths and null graphs are odd graceful. Finally, we present some examples
to illustrate the proposed theories.
We study QPT (quasi-polynomial tractability) in the worst case setting of linear tensor product problems defined over Hilbert spaces. We prove QPT for algorithms that use only function values under three assumptions'
1. the minimal errors for the univariate case decay polynomially fast to zero,
2. the largest singular value for the univariate case is simple,
3. the eigenfunction corresponding to the largest singular value is a multiple of the function value at some point.
The first two assumptions are necessary for QPT. The third assumption is necessary for QPT for some Hilbert spaces.
Joint work with Erich Novak
In [1] Abdel-Aal has introduced the notions of m-shadow graphs and n-splitting graphs, for all m, n ³ 1.
In this paper, we prove that, the m-shadow graphs for paths and complete bipartite graphs are odd
harmonious graphs for allm³ 1. Also, we prove the n-splitting graphs for paths, stars and symmetric
product between paths and null graphs are odd harmonious graphs for all n³ 1. In addition, we present
some examples to illustrate the proposed theories. Moreover, we show that some families of graphs admit
odd harmonious libeling.
In this paper, we show that the number of edges for any odd harmonious Eulerian graph is congruent to 0 or 2 (mod 4), and we found a counter example for the inverse of this statement is not true. We also proved that, the graphs which are constructed by two copies of even cycle Cn sharing a common edge are odd harmonious. In addition, we obtained an odd harmonious labeling for the graphs which are constructed by two copies of cycle Cn sharing a common vertex when n is congruent to 0 (mod 4). Moreover, we show that, the Cartesian product of cycle graph Cm and path Pn for each n ≥ 2, m ≡ 0 (mod 4) are odd harmonious graphs. Finally many new families of odd harmonious graphs are introduced.
Projection of a Vector upon a Plane from an Arbitrary Angle, via Geometric (C...James Smith
We show how to calculate the projection of a vector, from an arbitrary direction, upon a given plane whose orientation is characterized by its normal vector, and by a bivector to which the plane is parallel. The resulting solutions are tested by means of an interactive GeoGebra construction.
A Quest for Subexponential Time Parameterized Algorithms for Planar-k-Path: F...cseiitgn
The field of designing subexponential time parameterized algorithms has gained a lot of momentum lately. While the subexponential time algorithm for Planar-k-Path (finding a path of length at least k on planar graphs) has been known for last 15 years. There was no such algorithms known on directed planar graphs. In this talk, I will survey this journey of designing subexponential time parameterized algorithms for finding a path of length at least k in planar undirected graphs to planar directed graphs; highlighting the new tools and techniques that got developed on the way.
Gaps between the theory and practice of large-scale matrix-based network comp...David Gleich
I discuss some runtimes for the personalized PageRank vector and how it relates to open questions in how we should tackle these network based measures via matrix computations.
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
I am Irene M. I am a Stochastic Processes Assignment Expert at statisticsassignmenthelp.com. I hold a Master's in Statistics, from California, USA. I have been helping students with their homework for the past 6 years. I solve assignments related to Stochastic Processes.
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I am Manuela B. I am a Differential Equations Assignment Expert at mathsassignmenthelp.com. I hold a Master's in Mathematics from, the University of Warwick. I have been helping students with their assignments for the past 13 years. I solve assignments related to Differential Equations.
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I am Piers L. I am a Calculus Homework Solver at mathhomeworksolver.com. I hold a Master's in Mathematics From, the University of Adelaide. I have been helping students with their homework for the past 7 years. I solve homework related to Calculus.
Visit mathhomeworksolver.com or email support@mathhomeworksolver.com. You can also call on +1 678 648 4277 for any assistance with Calculus Homework.
I am Manuela B. I am a Calculus Assignment Expert at mathsassignmenthelp.com. I hold a Master's in Mathematics from, the University of Warwick Profession. I have been helping students with their assignments for the past 8 years. I solve assignments related to Calculus.
Visit mathsassignmenthelp.com or email info@mathsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Calculus Assignment.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Similar to Lego like spheres and tori, enumeration and drawings (20)
The computation of automorphic forms for a group Gamma is
a major problem in number theory. The only known way to approach the higher rank cases is by computing the action of Hecke operators on the cohomology.
Henceforth, we consider the explicit computation of the cohomology by using cellular complexes. We then explain how the rational elements can be made to act on the complex when it originate from perfect forms. We illustrate the results obtained for the symplectic Sp4(Z) group.
A crystallographic group is a group acting on R^n that contains a translation subgroup Z^n as a finite index subgroup. Here we consider which Coxeter groups are crystallographic groups. We also expose the enumeration in dimension 2 and 3. Then we shortly give the principle under which the enumeration of N dimensional crystallographic groups is done.
A strictly face regular map is a k-valent plane graph on the sphere or the entire plane with faces of size a and b such that any a-gonal face is adjacent to exactly p a-gonal face and exactly q b-gonal faces. If only one of such rule is respected then we get a weak face-regular map.
We present here enumeration technique for the face regular maps that rely on polycycle and other techniques.
Fullerenes are 3-valent plane graph that have have faces of size 5 or 6. This class of graph can be parametrized with 10 complex eisenstein numbers by Thurston theory. Here we consider spheric analogs of this theory and found 8 different classes. For each we consider following notions: (a) possible groups (b) Goldberg Coxeter construction (c) zigzags and central circuits (d) parameterization by complex integers.
Besides that we consider generalization to icosahedrites, space fullerenes and d-dimensional fullerenes.
A polycycle is a 2-connected plane locally finite graph G with faces partitioned
in two faces F1 and F2. The faces in F1 are combinatorial i-gons.
The faces in F2 are called holes and are pair-wise disjoint.
All vertices have degree {2,...,q} with interior vertices of degree q.
Polycycles can be decomposed into elementary polycycles. For some parameters (i,q) the elementary polycycles can be classified and this allows to solve many different combinatorial problems.
In a polytope P the faces F (from vertex to facets) define the combinatorics of P. In particular a flag F0, F1, ...., F(n-1) with Fi being a face of dimension i and Fi a subset of F(i+1).
From such a flag system and a subset S of {1,....,n} we can define a new flag system named the Wythoff construction. We consider the l1-embedding of the obtained graphs. We also expose an application of the Wythoff construction to the computation of homology of the Mathieu group M24.
Space fullerenes: A computer search of new Frank-Kasper structuresMathieu Dutour Sikiric
Fullerenes are 3-valent plane graphs with faces of size 5 or 6. A space fullerene is a tiling of Euclidean space with fullerene tiles. The space fullerenes occur in metallurgy, bubble foams, and the solution of the Kelvin problem. Here we present enumeration techniques that allows to find many new space fullerenes.
Implicit schemes are needed in order to have fast runtime in wave models. Parallelization using the Message Passing Interface are needed in order to run on computers with thousands of processors. Implicit schemes rely on preconditioner in order for the iterative schemes to converge fast. Thus we need fast preconditioners and we present those here.
The accurate modeling of the ocean requires the computation of the horizontal pressure gradient. This gradient depends on the difference of two large quantities and thus is susceptible to numerical errors. A way to avoid this to smooth the bathymetry. However, we do not want to perturb too much the bathymetry. Here we proposed to use linear programming in order to get a good representation of the bathymetry.
The Goldberg-Coxeter construction takes two integers (k,l) a 3-or 4-valent plane graph and returns a 3- or 4-valent plane graph. This construction is useful in virus study, numerical analysis, architecture, chemistry and of course mathematics.
Here we consider the zigzags and central circuits of 3- or 4-valent plane graph. It turns out that we can define an algebraic construction of (k,l)-product that allows to find the length of the zigzags and central circuits in a compact way. All possible lengths of zigzags are determined by this (k,l)-product and the normal structure of the automorphism group allows to find them for some congruence conditions.
Fullerene are 3-valent plane graphs with faces of size 5 or 6. They occur first in chemistry when C60 was synthetized. They are also interesting in mathematics for their intricate combinatorics with a parameterization of them by Thurston. In this whirling tour, we consider many context in which fullerenes occurs: viruses, zigags, face-regularity, tiling, crystallographic structures, etc.
Lattice coverings are a simple case of covering problems. We will first expose methods for finding the covering density of a given lattice. If one considers a space of possible lattices, then one gets the theory of L-type. We will explain how this theory works out and how the over a given L-type the problem is a
semidefinite programming problem. Finally, we will explore the covering maxima of lattices, i.e. local behavior of the covering density function.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
(May 29th, 2024) Advancements in Intravital Microscopy- Insights for Preclini...Scintica Instrumentation
Intravital microscopy (IVM) is a powerful tool utilized to study cellular behavior over time and space in vivo. Much of our understanding of cell biology has been accomplished using various in vitro and ex vivo methods; however, these studies do not necessarily reflect the natural dynamics of biological processes. Unlike traditional cell culture or fixed tissue imaging, IVM allows for the ultra-fast high-resolution imaging of cellular processes over time and space and were studied in its natural environment. Real-time visualization of biological processes in the context of an intact organism helps maintain physiological relevance and provide insights into the progression of disease, response to treatments or developmental processes.
In this webinar we give an overview of advanced applications of the IVM system in preclinical research. IVIM technology is a provider of all-in-one intravital microscopy systems and solutions optimized for in vivo imaging of live animal models at sub-micron resolution. The system’s unique features and user-friendly software enables researchers to probe fast dynamic biological processes such as immune cell tracking, cell-cell interaction as well as vascularization and tumor metastasis with exceptional detail. This webinar will also give an overview of IVM being utilized in drug development, offering a view into the intricate interaction between drugs/nanoparticles and tissues in vivo and allows for the evaluation of therapeutic intervention in a variety of tissues and organs. This interdisciplinary collaboration continues to drive the advancements of novel therapeutic strategies.
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
Lego like spheres and tori, enumeration and drawings
1. Lego like spheres and tori, enumeration and
drawings
Mathieu Dutour Sikiri´c
Rudjer Boskovi´c Institute,
Croatia
Michel Deza
Ecole Normale Sup´erieure,
France
November 24, 2017
3. ({a, b}, k)-maps
By a ({a, b}, k)-map, we mean a k-valent map of genus g
with faces of size a or b with a < b.
If g = 0 we speak of ({a, b}, k)-plane graph and if g = 1 we
speak of ({a, b}, k)-torus.
Euler-Poincar´e formula V − E + F = 2 − 2g can be
reformulated as
2k(2 − 2g) = {2k − a(k − 2)} pa + {2k − b(k − 2)} pb
We have essentially three cases for the plane graphs:
2k − b(k − 2) > 0 (Elliptic case): finite number of possibilities.
2k − b(k − 2) = 0 (Parabolic case): pa is constant
(independent of pb). Number of graphs growing polynomially
in pb.
2k − b(k − 2) < 0 (Hyperbolic case): pa growing with pb.
Number of graphs growing at least exponentially in pb
(conjecture)
4. List of parabolic cases
k (a, b) smallest one existence conn. pa v NrGr
3 (2, 6) Bundle3=3 × K2 p6 = T − 1 2 3 2 + 2p6 2
3 (3, 6) Tetrahedron p6 is even 2 or 3 4 4 + 2p6 5
3 (4, 6) Cube p6 = 1 3 6 8 + 2p6 16
3 (5, 6) Dodecahedron p6 = 1 3 12 20 + 2p6 28
4 (3, 4) Octahedron p4 = 1 3 8 6 + p4 18
4 (2, 4) Bundle4=4 × K2 p4 is even 2 4 2 + p4 5
6 (2, 3) Bundle6=6 × K2 p3 is even 2 6 2 + p3
2 22
6 (1, 3) Trifolium p3 = 2T − 1 1 3 1+p3
2 3
Notes:
T is a number of the form k2 + kl + l2
NrGr is the number of possible groups
A graph is k-connected is after removing k − 1 vertices it
remains connected.
5. Definition of lego
A ({a, b}, k)-map M admits a lego decomposition if there
exist a number m of cluster of faces such that the m clusters
put together yield the map M.
We impose in this work m = min(pa, pb). That is each cluster
has either just one a-gon or just one b-gon. This implies
pa
pb
∈ N or
pb
pa
∈ N
Examples:
68, T 8, C3 12, D5 44 D3h(D3)
6. When do lego exists?
Plane graph case:
In the elliptic cases we have a finite number of graphs to
consider. Easy.
In the parabolic cases:
If pa
pb
is integer then again a finite list of graphs to consider.
If pb
pa
is integer then we have an infinite set of possibilities and
existence can be proved in all of them.
In the hyperbolic cases:
If pb
pa
is integer then we can prove that there are only a finite
number of possibilities.
If pa
pb
is integer then a priori infinite number of possibilities but
existence is not proved.
Torus case:
If pb
pa
is integer then we can prove that there are only a finite
number of possibilities.
If pa
pb
is integer then a priori infinite number of possibilities but
existence is not proved.
7. Classification results I
For a hyperbolic ({a, b}, k)-sphere the number pb
pa
is an integer if
and only if its p-vector is either (p1, p3) = (k
2 , k
2 ), k ≥ 8, k ≡ 0
(mod 4) or one of 42 cases:
k a,b v (pa, pb)
3 3,7 20 (6,6)
3 3,7 68 (12,24)
3 3,8 44 (12,12)
3 4,7 44 (12,12)
3 2,7 12 (4,4)
3 2,7 32 (6,12)
3 2,7 92 (12,36)
3 2,8 20 (6,6)
3 2,9 44 (12,12)
4 2,5 14 (8,8)
5 2,4 12 (10,10)
7 2,3 16 (14,28)
k a,b v (pa, pb)
7 2,3 44 (28,84)
8 2,3 10 (16,16)
9 2,3 20 (36,36)
3 1,7 8 (3,3)
3 1,7 20 (4,8)
3 1,7 44 (6,18)
3 1,7 116 (12,48)
3 1,8 12 (4,4)
3 1,8 68 (12,24)
3 1,9 20 (6,6)
3 1,10 44 (12,12)
4 1,5 6 (4,4)
8. Classification results II
k a,b v (pa, pb)
4 1,5 22 (8,16)
4 1,6 14 (8,8)
5 1,4 4 (4,4)
5 1,4 52 (20,60)
5 1,5 12 (10,10)
6 1,4 5 (6,6)
7 1,3 4 (4,8)
7 1,3 16 (7,35)
7 1,3 44 (14,98)
k a,b v (pa, pb)
7 1,3 100 (28,224)
8 1,3 10 (8,24)
8 1,3 26 (16,64)
8 1,4 10 (16,16)
9 1,3 20 (18,54)
9 1,4 20 (36,36)
10 1,3 7 (10,20)
12 1,3 14 (24,48)
13 1,3 28 (52,104)
Notes:
Of those cases, only the ({1, 3}, 7)-spheres with 16 vertices
cannot be realized as a lego.
11. List of problems to be solved
Problem I is:
We have a list of pa a-gonal faces and pb b-gonal faces
We want to find all possible lego pieces
This is done, when possible, by exhaustive enumeration by
adding pieces one after the other in all configurations.
Problem II is:
We have a list of maps on the sphere or on torus
We want to find all legos that occur here.
This kind of enumeration is limited to the ({a, b}, k)-map
classes for which enumeration is feasible and there is a
program for it.
Problem III is:
We have a set of lego pieces
We want to find all the ways in which they can fit together.
This kind of method is a priori more clever since we build first
the list of pieces and then put them together.
12. List of feasible cases
The program CPF (by Thomas Harmuth, Master Thesis) can
enumerate the ({a, b}, 3)-spheres with a fixed number of
vertices and a ≥ 3, which are the most important cases.
The program CGF (by Thomas Harmuth, PhD Thesis) can
enumerate all the ({a, b}, 3)-maps of fixed genus and number
of vertices with a ≥ 3.
The program ENU can enumerate the ({a, b}, 4)-spheres with
fixed number of vertices and a ≥ 3.
The program plantri can do specific plane graph
enumeration but it is much slower and hard to use.
In all other cases, we are on our own to get the maps. Possible
methods is to reduce to one of the above classes. For some cases,
e.g. ({3, 7}, 3)-spheres with 68 vertices, the program cannot
terminate. Reductions are then needed.
13. Exact covering problem
Problem is:
Given n points and m subsets S1, . . . , Sm of {1, . . . , n}
to find all partitions of {1, . . . , n} by subsets Si .
Features:
The existence problem can be formulated as Integer
Programming Problem and it is NP.
It is an exhaustive enumeration problem and so harder a priori.
Fortunately, there exist the program LibExact by Kaski and
Pottonen which implements a very fast enumeration
procedure using “dancing links”.
It does not uses symmetry so we have to do isomorphism
checks afterwards.
14. Satisfiability problems SAT
A satisfiability problem (SAT) is a problem of the type:
A number n of variables v1, . . . , vn that can be true or false.
A number of clauses of the form
w1 ∨ w2 ∨ · · · ∨ wp with wj = vij
or vij
.
A set of clauses to be satisfied, i.e.
c1 ∧ c2 ∧ · · · ∧ cM.
The goal is to find whether there exist a set of variables that
satisfies all the clauses.
The program minisat can check satisfiability very fast despite
SAT being a NP problem. This allows to solve some combinatorial
problems. We can also enumerate all the solutions of a SAT
problem.
15. SAT for legos
SAT problems can be used to solve Sudoku, N-queens problems
and generally all kinds of combinatorial problems. What about
legos:
We take a set of N lego pieces, each identical and each having
p sides.
We need to put the condition of adjacency between the sides.
So, this makes about (Np)2 variables.
We have conditions around the edges since we want the
degree to be a specified value of say k.
But we cannot handle questions of connectivity.
In general the approach failed and this seems to be generally the
experience when using SAT to solve combinatorial problems such
as t-designs, distance regular graphs, etc.
16. Direct enumeration method
So, instead of SAT, we used a more classical enumeration method:
The idea is to take one lego and add pieces one at a time
until the obtained graph is complete.
In the case of place graph, one can prove that we can add the
pieces so that at all time the space that is not covered is
connected.
The method is typical backtrack enumeration and is all done
in C++.
Results:
The method generally works for up to say 8-12 lego pieces.
This allows to solve many cases.
18. Problematic
The problem that we have is how to represent a graph on the
plane or torus in a practical way.
The difficulty is how to represent 1-gons and 2-gons, which
most method do not.
Another issue is that many methods require the graph to be
3-connected, which is a strong requirement.
Additional wishes
We want the program to be as fast as possible. Drawing
should be a non-issue
We want details to be clearly visible.
We want the symmetries to be visible.
19. Representation of oriented maps
General maps are best represented via flag system (buildings,
chamber system, etc.)
For oriented maps, we can use a simpler yet equivalent
system: directed edge.
Directed edge are basically a pair (v, e) with v a vertex and e
an edge.
Given a directed edge −→e we can build the next directed edge
n(−→e ) around the vertex (in trigonometric order) and the
inverse directed edge i(−→e )
Vertices, edges and faces the correspond to the orbits of the
permutations n, i and n ◦ i on the set of directed edges.
Example:
16
8 11 4 9 2 15 14 13 0 3 12 1 10 7 6 5
1 2 3 0 5 6 7 4 9 10 11 8 13 14 15 12
20. Existing approaches
Tutte: He proposed to use eigenvectors of the adjacency
matrix in order to provide embeddings. The method works
well for plane graphs but suffer from one key problem: the
inner faces tend to be very small and not visible. Only for
plane graphs.
Dress,Harmuth,Delgado Friedrichs,Brinkmann: The CaGe
program uses an iterative process in order to get the
embedding. A priori only for plane graphs.
Mohar: Primal-Dual circle packings provide a good theoretical
based approach for finding the embeddings. It works for plane
graph, torus and hyperbolic maps.
Force directed graphs. A physical functional such as
F =
e=(i,j)∈E(G)
f ( xi − xj )
and we minimize over the embedding.
21. Issues and features
Features:
All above techniques will respect symmetries since they are
based on minimization procedure. But sometimes the number
of iterations needs to be adjusted.
All coordinates are obtained by iteration procedures. We
cannot do exact arithmetic computations.
Issues:
Some technique requires 3-connectivity of the graph
All fail to work for 2-gons and 1-gons.
Convergence might take a long time to achieve.
Some details of the graph might be very hard to see in the
final drawing. According to the cases
For the plane graph, one factor is the proximity to the exterior
face, another is the level of refinement.
For the torus, it is flat so the only problem is the level of
refinement.
For the hyperbolic plane, the problem will necessarily occur in
all reasonable representations such as Poincar´e plane or similar.
22. Primal-Dual circle packings
The idea is to put circles in the vertex center and faces such that
If any two vertices v and v are adjacent then the
corresponding circles are tangent.
For any face the circle is tangent to the edges.
v w
f
g
The local picture of a
primal-dual circle
representation
The edges, circle and face
circles of a primal-dual
representation
23. Primal-Dual circle packings: Equations and Numerics
In the case of torus, the equations that are satisfied are
π = φv =
uv∈E(Med∗(G))
arctan
ru
rv
for each vertex v of the dual medial graph of G.
Bojan Mohar has given an algorithm for computing primal
dual circle packings. It consists of computing the defect at
every node and increasing/decreasing the radius value
according to φv > π or φv < π. It is a geometric method but
in some cases it is very slow.
Instead our approach is to use a variant of Newton method:
We choose the direction of change from the Newton iteration
solver and we adjust the amount of change so that we remain
in the allowed region of circles of positive radius.
x(n+1)
= x(n)
− c
f (x(n))
f (x(n))
with 0 < c ≤ 1
24. Refinement techniques
The primal-dual technique requires 3-connectivity and will not
work with 2-gons and 1-gons.
The technique is to refine it. First for a map M we replace it
with the order complex map Ord(M) = Trunc(Med(M)).
Then we insert a vertex and each edge.
Finally, we put a vertex on each face and connect it with all
incident vertices.
The resulting triangulation is 3-connected.
25. Symmetric representation
For plane graph, we want to represent the maps with the
maximum amount of symmetry.
In practical matter if we have an axis of symmetry of order N
then we want it visible.
If the axis pass by a vertex or an edge then we put it to
infinity.
Examples:
On vertex On edge On face
26. CaGe process
Suppose that we have a point x and m adjacent points x1,
. . . , xm then for the CaGe process we have the equation
x =
1
m
i=1 A2
T (x, xi , xi+1)
m
i=1
A2
T (x, xi
, xi+1
)
x + xi + xi+1
3
with AT (x, y, z) the area of the triangle of vertices x, y and z.
The equation is solved by fixed point iterations.
Plane graph: put the vertices of the exterior face in a circle.
Torus map: first guess obtained by primal dual circle packing
and then apply the CaGe process.
27. Problem of 1-gons
Our approach of auxiliary graphs works fairly well with 2-gons.
But with 1-gons, we tend to get far smaller faces than
expected.
The empirical solution is to rescale the 1-gons by large factors
(say 200) so that they become visible.
normal expanded
28. Software availability
Source code is available at
https://github.com/MathieuDutSik/Plot orientedmap
Code written in C++11 language.
Uses the Eigen library for matrix computations.
Input file in Namelist, fortran style input.
Output file in svg (Scalable Vector Graphics) to be used on
web page or in Inkscape.