cometadata/datacite-rtg-text-other-reclassification-records huggingface dataset:
Wetting and layering for Solid-on-Solid I: Identification of the wetting point and critical behavior
Creators: name: Lacoin, Hubert
Publisher: name: arXiv
Year: 2017
Subjects: subject: Mathematical Physics (math-ph)
subject: Probability (math.PR)
subject: FOS: Physical sciences
subject: FOS: Mathematics

description: We provide a complete description of the low temperature wetting transition for the two dimensional Solid-On-Solid model. More precisely we study the integer-valued field $(ϕ(x))_{x\in \mathbb Z^2}$, associated associated to the energy functional $$V(ϕ)=β\sum_{x\sim y}|ϕ(x)-ϕ(y)|-\sum_{x}\left(h{\bf 1}_{\{ϕ(x)=0\}}-\infty{\bf 1}_{\{ϕ(x)<0\}} \right).$$ It is known since the pioneering work of Chalker (J. Phys. A {\bf 15} (1982) 481-485) that for every $β$, there exists $h_{w}(β)>0$ delimiting a transition between a delocalized phase ($hh_{w}(β)$) where this proportion is positive. We prove in the present paper that for $β$ sufficiently large we have $$h_w(β)= \log \left(\frac{e^{4β}}{e^{4β}-1}\right).$$ Furthermore we provide a sharp asymptotic for the free energy at the vicinity of the critical point: We show that close to $h_w(β)$, the free energy is approximately piecewise affine and that the points of discontinuity for the derivative of the affine approximation forms a geometric sequence accumulating on the right of $h_w(β)$. This asymptotic behavior provides a strong evidence for the conjectured existence of countably many "layering transitions" at the vicinity of the critical point, corresponding to jumps for the typical height of the field.
description: 39 pages, 4 Figures
Firenze nella Storia
Creators: name: AA. VV.
Publisher: name: Zenodo
Year: 2022

description: "Firenze nella Storia" nasce con lo scopo di approfondire il ruolo di Firenze nella civiltà, nella cultura, nell'arte nel corso dei secoli, senza particolari delimitazioni cronologiche o tematiche. Il progetto, inserendosi nel solco delle Digital & Public Humanities, intende coniugare alta divulgazione e ricerca e si propone come cantiere interdisciplinare aperto alla collaborazione di tutti gli interessati (singole persone come enti e istituzioni, se interessati), sul modello di precedenti e fortunate esperienze promosse dall'Associazione e dalle Edizioni CLORI quali i portali Ereticopedia, con il suo Dizionario di eretici, dissidenti e inquisitori nel mondo mediterraneo, e "Storia della Campania". Prendiamo spunto altresì dall'esperienza di precedenti portali di storia della città e del territorio, che hanno avuto alterne fortune fino alla loro cessazione, quali "Storia di Venezia" (www.storiadivenezia.net) o, ancor più specificamente, "Storia di Firenze" (www.storiadifirenze.org), impegnandoci tuttavia a mantenere in vita molto più a lungo, se non perennemente, il presente progetto, che ha il vantaggio di sostenersi da solo, fondandosi su una struttura snella e su modelli ben sperimentati, senza bisogno assoluto di finanziamenti costanti, di collaboratori stipendiati ad hoc e/o di particolari appoggi istituzionali. Perché questo progetto possa svilupparsi compiutamente, contiamo soprattutto di attrarre persone unite dalla passione e dell'impegno civile, com'è accaduto per Ereticopedia e per Storia della Campania, la cui riuscita ci fa credere che anche questa volta la nostra scommessa potrà essere vincente.
Generalized TMDs and the exclusive double Drell-Yan process
Creators: name: Bhattacharya, Shohini
name: Metz, Andreas
name: Zhou, Jian
Publisher: name: arXiv
Year: 2017
Subjects: subject: High Energy Physics - Phenomenology (hep-ph)
subject: High Energy Physics - Experiment (hep-ex)
subject: Nuclear Experiment (nucl-ex)
subject: FOS: Physical sciences

description: Generalized transverse momentum dependent parton distributions (GTMDs) are the most general parton correlation functions of hadrons. By considering the exclusive double Drell-Yan process it is shown for the first time how quark GTMDs can be measured. Specific GTMDs can be addressed by means of polarization observables.
description: 6 pages, 1 figure, typos fixed
Analysis of nonlocal phonon thermal conductivity simulations showing the ballistic to diffusive crossover
Creators: name: Allen, Philip B.
Publisher: name: arXiv
Year: 2016
Subjects: subject: Materials Science (cond-mat.mtrl-sci)
subject: FOS: Physical sciences

description: Simulations (e.g. Zhou et al., Phys. Rev. B 79, 115201 (2009)) show nonlocal effects of the ballistic/diffusive crossover. The local temperature has nonlinear spatial variation not contained in the local Fourier law $\vec{j}(\vec{r})=-κ\vec{\nabla}T(\vec{r})$. The heat current $\vec{j}(\vec{r})$ depends not just on the local temperature gradient $\vec{\nabla}T(\vec{r})$, but also on temperatures at points $\vec{r}^{ \ \prime}$ within phonon mean free paths, which can be micrometers long. This paper uses the Peierls-Boltzmann transport theory in non-local form to analyze the spatial variation $ΔT(\vec{r})$. The relaxation-time approximation (RTA) is used because full solution is very challenging. Improved methods of extrapolation to obtain the bulk thermal conductivity $κ$ are proposed. Callaway invented an approximate method of correcting RTA for the $\vec{q}$ (phonon wavevector or crystal momentum) conservation of N (normal as opposed to Umklapp) anharmonic collisions This method is generalized to the non-local case where $κ(\vec{k})$ depends on wavevector of the current $\vec{j}(\vec{k})$ and temperature gradient $i\vec{k}ΔT(\vec{k})$.
description: 10 pages and 5 figures. This new version replaces the versions from April 2017 and March 2018. The source term is included in the Boltzmann equation, for the heat driving the phonon distribution. This method agrees with other recent work, and gives a better fit to the simulation of kappa(k). Recent changes are a clearer presentation thanks to help from an anonymous referee
Polynomial Wolff axioms and Kakeya-type estimates in $\mathbb{R}^4$
Creators: name: Guth, Larry
name: Zahl, Joshua
Publisher: name: arXiv
Year: 2017
Subjects: subject: Classical Analysis and ODEs (math.CA)
subject: FOS: Mathematics

description: We establish new linear and trilinear bounds for collections of tubes in $\mathbb{R}^4$ that satisfy the polynomial Wolff axioms. In brief, a collection of $δ$-tubes satisfies the Wolff axioms if not too many tubes can be contained in the $δ$-neighborhood of a plane. A collection of tubes satisfies the polynomial Wolff axioms if not too many tubes can be contained in the $δ$-neighborhood of a low degree algebraic variety. First, we prove that if a set of $δ^{-3}$ tubes in $\mathbb{R}^4$ satisfies the polynomial Wolff axioms, then the union of the tubes must have volume at least $δ^{1-1/40}$. We also prove a more technical statement which is analogous to a maximal function estimate at dimension $3+1/40$. Second, we prove that if a collection of $δ^{-3}$ tubes in $\mathbb{R}^4$ satisfies the polynomial Wolff axioms, and if most triples of intersecting tubes point in three linearly independent directions, then the union of the tubes must have volume at least $δ^{3/4}$. Again, we also prove a slightly more technical statement which is analogous to a maximal function estimate at dimension $3+1/4$. We conjecture that every Kakeya set satisfies the polynomial Wolff axioms, but we are unable to prove this. If our conjecture is correct, it implies a Kakeya maximal function estimate at dimension $3+1/40$, and in particular this implies that every Kakeya set in $\mathbb{R}^4$ must have Hausdorff dimension at least $3+1/40$. This would be an improvement over the current best bound of 3, which was established by Wolff in 1995.
description: 30 pages, 0 figures. v3: An error has been corrected, which weakens the dimension of our maximal function estimate to 3 + 1/40. Previously, a bound of 3 + 1/28 was claimed. See the addendum following the statement of Theorem 1.1 for details
Fractional quantum Hall effect in the interacting Hofstadter model via tensor networks
Creators: name: Gerster, Matthias
name: Rizzi, Matteo
name: Silvi, Pietro
name: Dalmonte, Marcello
name: Montangero, Simone
Publisher: name: arXiv
Year: 2017
Subjects: subject: Quantum Gases (cond-mat.quant-gas)
subject: Strongly Correlated Electrons (cond-mat.str-el)
subject: Quantum Physics (quant-ph)
subject: FOS: Physical sciences

description: We show via tensor network methods that the Harper-Hofstadter Hamiltonian for hard-core bosons on a square geometry supports a topological phase realizing the $ν=1/2$ fractional quantum Hall effect on the lattice. We address the robustness of the ground state degeneracy and of the energy gap, measure the many-body Chern number, and characterize the system using Green functions, showing that they decay algebraically at the edges of open geometries, indicating the presence of gapless edge modes. Moreover, we estimate the topological entanglement entropy by taking a combination of lattice bipartitions that reproduces the topological structure of the original proposals by Kitaev and Preskill, and Levin and Wen. The numerical results show that the topological contribution is compatible with the expected value $γ= 1/2$. Our results provide extensive evidence that FQH states are within reach of state-of-the-art cold atom experiments.
description: 9 pages, 11 figures; close to published version
Characterization and Expression Analysis of the Calmodulin Protein, CAM2, in Arabidopsis Thaliana
Creators: name: Pandey, Soumili
Publisher: name: Zenodo
Year: 2023
Subjects: CAM2
Arabidopsis Thaliana
Gene Expression
Biotic Stress
Translation
Expression Analysis

description: Calmodulin is an intermediate calcium binding receptor messenger protein expressed in every eukaryotic cells. This is a very important factor in the Arabidopsis thaliana. Characterization and expression analysis of CAM2 were conducted to obtain important information of its function and regulation control under several stress condition. The study included ePlant heat map representation data, GO and KEGG analysis pathway interpretation. ePlant data gives us the insights of various tissue specific and cellular localization through heat map data. GO analysis data gives us inputs about molecular function, biological processes and cellular components. KEGG pathway analysis data represents how CAM2 expresses over any stress condition, how it is related with various conserved signalling pathways. Overall, these findings give us the answer that how each and every, environmental factors are connected with each other and how these organisms act upon certain environmental factors. The one of the most important findings from this characterization and expression analysis were, CAM2 is very important to response to several biotic factors such as pathogen interaction. CAM2 is highly responsible for the growth of mature pollen of Arabidopsis thaliana.
title: ИСТОРИЧЕСКИЕ ГОРОДА ГЛАЗАМИ КРУИЗНОГО ТУРИСТА
Creators: name: Рожков, Кирилл
Publisher: name: Новгородский государственный университет имени Ярослава Мудрого (НовГУ)
Year: 2022

description: Ограничения выездного туризма в связи с пандемией и геополитической ситуацией перенаправили туристической поток внутрь страны и создали возможность для малых исторических городов заработать на приёме гостей. Многолетний успешный опыт Мышкина по привлечению круизных туристов был до последнего времени описан преимущественно в гуманитарных исследованиях, но не получил необходимого осмысления в терминах маркетинга и менеджмента. Целью настоящего исследования является выявление факторов успеха города Мышкина в развитии круизного туризма. Применённый метод исследования – множественное кейс-стади. Для сбора данных использовалась совокупность методов невключённого (внутреннего) этнографического наблюдения и «тайного покупателя». Результаты анализа позволили выявить сравнительные преимущества Мышкина в управлении городом как туристической дестинацией.
FFPDG: Fast, Fair and Private Data Generation
Creators: name: Xu, Weijie
name: Zhao, Jinjin
name: Iannacci, Francis
name: Wang, Bo
Publisher: name: arXiv
Year: 2023
Subjects: subject: Machine Learning (cs.LG)
subject: Artificial Intelligence (cs.AI)
subject: FOS: Computer and information sciences
subject: 94-10

description: Generative modeling has been used frequently in synthetic data generation. Fairness and privacy are two big concerns for synthetic data. Although Recent GAN [\cite{goodfellow2014generative}] based methods show good results in preserving privacy, the generated data may be more biased. At the same time, these methods require high computation resources. In this work, we design a fast, fair, flexible and private data generation method. We show the effectiveness of our method theoretically and empirically. We show that models trained on data generated by the proposed method can perform well (in inference stage) on real application scenarios.
description: 12 pages, 2 figures, ICLR 2021 Workshop on Synthetic Data Generation
Constructing an expanding metric for dynamical systems in one complex variable
Creators: name: Hruska, Suzanne Lynch
Publisher: name: arXiv
Year: 2004
Subjects: subject: Dynamical Systems (math.DS)
subject: FOS: Mathematics
subject: 37F15, 37F10, 37F50, 37B35, 37-04

description: We describe a rigorous computer algorithm for attempting to construct an explicit, discretized metric for which a complex polynomial map is expansive on a given neighborhood of its Julia set. We show construction of such a metric proves the map is hyperbolic. We also examine the question of whether the algorithm can be improved, and the related question of how to build a metric as close to euclidean as possible. Finally, we give several examples generated with our implementation of this algorithm.
description: 18 pages. 8 figures. Revised version (intro. restructured, some minor clarifications through rest)
Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm
Creators: name: Fischer, Simon
name: Steinwart, Ingo
Publisher: name: arXiv
Year: 2017
Subjects: subject: Machine Learning (stat.ML)
subject: FOS: Computer and information sciences

description: Learning rates for least-squares regression are typically expressed in terms of $L_2$-norms. In this paper we extend these rates to norms stronger than the $L_2$-norm without requiring the regression function to be contained in the hypothesis space. In the special case of Sobolev reproducing kernel Hilbert spaces used as hypotheses spaces, these stronger norms coincide with fractional Sobolev norms between the used Sobolev space and $L_2$. As a consequence, not only the target function but also some of its derivatives can be estimated without changing the algorithm. From a technical point of view, we combine the well-known integral operator techniques with an embedding property, which so far has only been used in combination with empirical process arguments. This combination results in new finite sample bounds with respect to the stronger norms. From these finite sample bounds our rates easily follow. Finally, we prove the asymptotic optimality of our results in many cases.
description: accepted manuscript in J. Mach. Learn. Res
Rigorous numerical studies of the dynamics of polynomial skew products of C^2
Creators: name: Hruska, Suzanne Lynch
Publisher: name: arXiv
Year: 2005
Subjects: subject: Dynamical Systems (math.DS)
subject: FOS: Mathematics
subject: 32H50

description: For the class of polynomial skew products of C^2, we describe a rigorous computer algorithm which, for a given map F, will (1) build a model of the dynamics of F on its chain recurrent set, and (2) attempt to determine whether F is Axiom A. Further, we discuss how we used our implementation of this algorithm to establish Axiom A for several explicit cases.
description: 15 pages, 12 figures, submitted
Modelling and Analysis of Quantum Key Distribution Protocols, BB84 and B92, in Communicating Quantum Processes(CQP) language and Analysing in PRISM
Creators: name: Kuppam, Satya
Publisher: name: arXiv
Year: 2016
Subjects: subject: Cryptography and Security (cs.CR)
subject: Quantum Physics (quant-ph)
subject: FOS: Computer and information sciences
subject: FOS: Physical sciences

description: Proof of security of cryptographic protocols theoretically establishes the strength of a protocol and the constraints under which it can perform, it does not take into account the overall design of the protocol. In the past model checking has been successfully applied to classical cryptographic protocols to weed out design flaws which would have otherwise gone unnoticed. Quantum cryptographic protocols differ from their classical counterparts, in their ability to detect the presence of an eavesdropper. Although unconditional security has been proven for both BB84 and B92 protocols, in this paper we show that identifying an eavesdropper's presence is constrained on the number of qubits exchanged. We first model the protocols in CQP and then explain the mechanism by which we have translated this into a PRISM model. We mainly focus on the protocols' ability to detect an active eavesdropper and the extent to which an eavesdropper can retrieve the shared key without being detected by either party. We then conclude by comparing the performance of the protocols.
description: 12 pages, 21 figures, bachelor thesis work
Persistence of the N = 50 shell closure over the isotopic chains of Sc, Ti, V and Cr nuclei using relativistic energy density functional
Creators: name: Yadav, Praveen K.
name: Kumar, Raj
name: Bhuyan, M.
Publisher: name: arXiv
Year: 2024
Subjects: subject: Nuclear Theory (nucl-th)
subject: Computational Physics (physics.comp-ph)
subject: FOS: Physical sciences

description: The analytical expression of the density-dependent binding energy per nucleon for the relativistic mean field (RMF), also known as the relativistic energy density functional (Relativistic-EDF), is used to obtain the isospin-dependent symmetry energy and its components for the isotopic chain of Sc, Ti, V, and Cr nuclei. The procedure of the coherent density fluctuation model is employed to formulate the Relativistic-EDF and Brueckner energy density functional (Brueckner-EDF) at local density. A few signatures of shell and/or sub-shell closure are observed in the symmetry energy and its components, i.e., surface and volume symmetry energy, far from the beta-stable region for odd-A Sc and V, and even-even Ti and Cr nuclei with non-linear NL3 and G3 parameter sets. A comparison is made with the results obtained from Relativistic-EDF and Brueckner-EDF with both NL3 and G3 for the considered isotopic chains. We find Relativistic-EDF outperforms the Brueckner-EDF in predicting the shell and/or sub-shell closure of neutron-rich isotopes at N = 50 for these atomic nuclei. Moreover, a relative comparison has been made for the results obtained with the non-linear NL3 and G3 parameter sets.
description: 18 pages, 4 figures
Geometric Bijections for Regular Matroids, Zonotopes, and Ehrhart Theory
Creators: name: Backman, Spencer
name: Baker, Matthew
name: Yuen, Chi Ho
Publisher: name: arXiv
Year: 2017
Subjects: subject: Combinatorics (math.CO)
subject: FOS: Mathematics

description: Let $M$ be a regular matroid. The Jacobian group ${\rm Jac}(M)$ of $M$ is a finite abelian group whose cardinality is equal to the number of bases of $M$. This group generalizes the definition of the Jacobian group (also known as the critical group or sandpile group) ${\rm Jac}(G)$ of a graph $G$ (in which case bases of the corresponding regular matroid are spanning trees of $G$). There are many explicit combinatorial bijections in the literature between the Jacobian group of a graph ${\rm Jac}(G)$ and spanning trees. However, most of the known bijections use vertices of $G$ in some essential way and are inherently "non-matroidal". In this paper, we construct a family of explicit and easy-to-describe bijections between the Jacobian group of a regular matroid $M$ and bases of $M$, many instances of which are new even in the case of graphs. We first describe our family of bijections in a purely combinatorial way in terms of orientations; more specifically, we prove that the Jacobian group of $M$ admits a canonical simply transitive action on the set ${\mathcal G}(M)$ of circuit-cocircuit reversal classes of $M$, and then define a family of combinatorial bijections $β_{σ,σ^*}$ between ${\mathcal G}(M)$ and bases of $M$. (Here $σ$ (resp. $σ^*$) is an acyclic signature of the set of circuits (resp. cocircuits) of $M$.) We then give a geometric interpretation of each such map $β=β_{σ,σ^*}$ in terms of zonotopal subdivisions which is used to verify that $β$ is indeed a bijection. Finally, we give a combinatorial interpretation of lattice points in the zonotope $Z$; by passing to dilations we obtain a new derivation of Stanley's formula linking the Ehrhart polynomial of $Z$ to the Tutte polynomial of $M$.
description: v2: 39 pages, 5 figures, include a partial extension to realizable oriented matroids (cf. Section 1.5); v3: improved exposition
Periodic quantum graphs from the Bethe-Sommerfeld perspective
Creators: name: Exner, Pavel
name: Turek, Ondřej
Publisher: name: arXiv
Year: 2017
Subjects: subject: Mathematical Physics (math-ph)
subject: Spectral Theory (math.SP)
subject: Quantum Physics (quant-ph)
subject: FOS: Physical sciences
subject: FOS: Mathematics
subject: 81Q35 (Primary) 35J10, 34L40, 11K60 (Secondary)

description: The paper is concerned with the number of open gaps in spectra of periodic quantum graphs. The well-known conjecture by Bethe and Sommerfeld (1933) says that the number of open spectral gaps for a system periodic in more than one direction is finite. To the date its validity is established for numerous systems, however, it is known that quantum graphs do not comply with this law as their spectra have typically infinitely many gaps, or no gaps at all. These facts gave rise to the question about the existence of quantum graphs with the `Bethe-Sommerfeld property', that is, featuring a nonzero finite number of gaps in the spectrum. In this paper we prove that the said property is impossible for graphs with the vertex couplings which are either scale-invariant or associated to scale-invariant ones in a particular way. On the other hand, we demonstrate that quantum graphs with a finite number of open gaps do indeed exist. We illustrate this phenomenon on an example of a rectangular lattice with a $δ$ coupling at the vertices and a suitable irrational ratio of the edges. Our result allows to find explicitly a quantum graph with any prescribed exact number of gaps, which is the first such example to the date.
description: 33 pages, 1 figure; revised version, text partly rewritten, explanations added
Investigations on assembly and coverage for modular focal planes of multiplexed telescopes
Creators: name: Rombach, Maxime
name: Xu, Xiangyu
name: Araujo, Ricardo
name: Thurneysen, Markus
name: Caseiro, Stefane
name: Magnenat, Corentin
name: Silber, Joseph H.
name: Galal, Malak
name: Schlegel, David
name: Kneib, Jean-Paul
Publisher: name: arXiv
Year: 2024
Subjects: subject: Instrumentation and Methods for Astrophysics (astro-ph.IM)
subject: FOS: Physical sciences

description: Multiplexed surveys have the ambition to grow larger for the next generation of focal plane instruments. Future projects such as Spec-S5, MUST, and WST have an ever-growing need for multi-object spectroscopy (13,000 - 20,000 simultaneous objects) which demands further investigations of novel focal plane instrumentation. In this paper, we present a rigorous study of focal plane coverage optimization and assembly of triangular modules of alpha-beta fiber positioners with a 6.2 mm pitch. The main focus here is to examine different module arrangements namely, framed, semi-frameless, and fullyframeless assemblies. Framed and semi-frameless describe here the usage of a manufactured focal plate to hold the modules together and provide the correct focus and tilt to the fibers. Work on automatically generating such focal plates for project adaptability and ease of manufacturing will also be presented. On the other hand, the frameless approach proposes a connection method freed from the need of a focal plate. The following paper will also present their capabilities to meet the requirements for focal plane assembly such as focus, tilt and coverage.
description: 16 pages, 16 figures, SPIE Astronomical Telescopes + Instrumentation 2024
Analogue Stochastic Gravity in Strongly-Interacting Bose-Einstein Condensates
Creators: name: Keser, Aydin Cem
name: Galitski, Victor
Publisher: name: arXiv
Year: 2016
Subjects: subject: Quantum Gases (cond-mat.quant-gas)
subject: Statistical Mechanics (cond-mat.stat-mech)
subject: General Relativity and Quantum Cosmology (gr-qc)
subject: FOS: Physical sciences

description: Collective modes propagating in a moving superfluid are known to satisfy wave equations in a curved space time, with a metric determined by the underlying superflow. We use the Keldysh technique in a curved space-time to develop a quantum geometric theory of fluctuations in superfluid hydrodynamics. This theory relies on a 'quantized' generalization of the two-fluid description of Landau and Khalatnikov, where the superfluid component is viewed as a quasi-classical field coupled to a normal component -- the collective modes/phonons representing a quantum bath. This relates the problem in the hydrodynamic limit to the 'quantum friction' problem of Caldeira-Leggett type. By integrating out the phonons, we derive stochastic Langevin equations describing a coupling between the superfluid component and phonons. These equations have the form of Euler equations with additional source terms expressed through a fluctuating stress-energy tensor of phonons. Conceptually, this result is similar to stochastic Einstein equations that arise in the theory of stochastic gravity. We formulate the fluctuation-dissipation theorem in this geometric language and discuss possible physical consequences of this theory.
description: 19 pages, 2 figures
A geometrical imaging of the real gap between economies of China and the United States
Creators: name: Hosseiny, Ali
Publisher: name: arXiv
Year: 2017
Subjects: subject: General Finance (q-fin.GN)
subject: Physics and Society (physics.soc-ph)
subject: General Economics (econ.GN)
subject: FOS: Economics and business
subject: FOS: Physical sciences

description: GDP of China is about 11 trillion dollars and GDP of the United States is about 18 trillion dollars. Suppose that we know for the coming years, economy of the US will experience a real growth rate equal to \%3 and economy of China will experience a real growth as of \%6. Now, the question is how long does it take for economy of China to catch the economy of the United States. The early impression is that the desired time is the answer of the equation $11\times1.06^X=18\times1.03^X$. The correct answer however is quite different. GDP is not a simple number and the gap between two countries can not be addressed simply through their sizes. It is rather a geometrical object. Countries pass different paths in the space of production. The gaps between GDP of different countries depend on the path that each country passes through and local metric. To address distance between economies of China and of the US we need to know their utility preferences and the path that China passes to reach the US size. The true gap then can be found if we calculate local metric along this path. It resembles impressions about measurements in the General Theory of Relativity. Path dependency of aggregate indexes is widely discussed in the Index Number Theory. Our aim is to stick to the geometrical view presented in the General Relativity to provide a visual understanding of the matter. We show that different elements in the general relativity have their own counterparts in economics. We claim that national agencies who provide aggregate data resemble falling observers into a curved space time. It is while the World Bank or international organizations are outside observers. The vision provided here, leaves readers with a clear conclusion. If China keeps its growth rate, then the economy of China should catch the economy of the United States sooner than what we expect.
Projected Tensor Power Method for Hypergraph Community Recovery
Creators: name: Wang, Jinxin
name: Pun, Yuen-Man
name: Wang, Xiaolu
name: Wang, Peng
name: So, Anthony Man-Cho
Publisher: name: arXiv
Year: 2023
Subjects: subject: Optimization and Control (math.OC)
subject: FOS: Mathematics

description: This paper investigates the problem of exact community recovery in the symmetric $d$-uniform $(d \geq 2)$ hypergraph stochastic block model ($d$-HSBM). In this model, a $d$-uniform hypergraph with $n$ nodes is generated by first partitioning the $n$ nodes into $K\geq 2$ equal-sized disjoint communities and then generating hyperedges with a probability that depends on the community memberships of $d$ nodes. Despite the non-convex and discrete nature of the maximum likelihood estimation problem, we develop a simple yet efficient iterative method, called the \emph{projected tensor power method}, to tackle it. As long as the initialization satisfies a partial recovery condition in the logarithmic degree regime of the problem, we show that our proposed method can exactly recover the hidden community structure down to the information-theoretic limit with high probability. Moreover, our proposed method exhibits a competitive time complexity of $\mathcal{O}(n\log^2n/\log\log n)$ when the aforementioned initialization condition is met. We also conduct numerical experiments to validate our theoretical findings.
The Kontsevich integral for bottom tangles in handlebodies
Creators: name: Habiro, Kazuo
name: Massuyeau, Gwenael
Publisher: name: arXiv
Year: 2017
Subjects: subject: Geometric Topology (math.GT)
subject: Quantum Algebra (math.QA)
subject: FOS: Mathematics
subject: 57M27, 18D10, 19D23, 17B37

description: Using an extension of the Kontsevich integral to tangles in handlebodies similar to a construction given by Andersen, Mattes and Reshetikhin, we construct a functor $Z:\mathcal{B}\to \widehat{\mathbb{A}}$, where $\mathcal{B}$ is the category of bottom tangles in handlebodies and $\widehat{\mathbb{A}}$ is the degree-completion of the category $\mathbb{A}$ of Jacobi diagrams in handlebodies. As a symmetric monoidal linear category, $\mathbb{A}$ is the linear PROP governing "Casimir Hopf algebras", which are cocommutative Hopf algebras equipped with a primitive invariant symmetric 2-tensor. The functor $Z$ induces a canonical isomorphism $\hbox{gr}\mathcal{B} \cong \mathbb{A}$, where $\hbox{gr}\mathcal{B}$ is the associated graded of the Vassiliev-Goussarov filtration on $\mathcal{B}$. To each Drinfeld associator $φ$ we associate a ribbon quasi-Hopf algebra $H_φ$ in $\hbox{gr}\mathcal{B}$, and we prove that the braided Hopf algebra resulting from $H_φ$ by "transmutation" is precisely the image by $Z$ of a canonical Hopf algebra in the braided category $\mathcal{B}$. Finally, we explain how $Z$ refines the LMO functor, which is a TQFT-like functor extending the Le-Murakami-Ohtsuki invariant.
description: 84 pages; only minor changes in this final version
Squaring parametrization of constrained and unconstrained sets of quantum states
Creators: name: Il'in, N.
name: Shpagina, E.
name: Uskov, F.
name: Lychkovskiy, O.
Publisher: name: arXiv
Year: 2017
Subjects: subject: Quantum Physics (quant-ph)
subject: FOS: Physical sciences

description: A mixed quantum state is represented by a Hermitian positive semi-definite operator $ρ$ with unit trace. The positivity requirement is responsible for a highly nontrivial geometry of the set of quantum states. A known way to satisfy this requirement automatically is to use the map $ρ=τ^2 / \mathrm {tr} \, τ^2$, where $τ$ can be an arbitrary Hermitian operator. We elaborate a parametrization of the set of quantum states induced by the parametrization of the linear space of Hermitian operators by virtue of this map. In particular, we derive an equation for the boundary of the set. Further, we discuss how this parametrization can be applied to a set of quantum states constrained by some symmetry, or, more generally, some linear condition. As an example, we consider the parametrization of sets of Werner states of qubits.
Sparse Signal Reconstruction for Overdispersed Low-photon Count Biomedical Imaging Using $\ell_p$ Total Variation
Creators: name: Lu, Yu
name: Marcia, Roummel F.
Publisher: name: arXiv
Year: 2024
Subjects: subject: Image and Video Processing (eess.IV)
subject: Computer Vision and Pattern Recognition (cs.CV)
subject: Signal Processing (eess.SP)
subject: Optimization and Control (math.OC)
subject: FOS: Electrical engineering, electronic engineering, information engineering
subject: FOS: Computer and information sciences
subject: FOS: Mathematics

description: The negative binomial model, which generalizes the Poisson distribution model, can be found in applications involving low-photon signal recovery, including medical imaging. Recent studies have explored several regularization terms for the negative binomial model, such as the $\ell_p$ quasi-norm with $0 < p < 1$, $\ell_1$ norm, and the total variation (TV) quasi-seminorm for promoting sparsity in signal recovery. These penalty terms have been shown to improve image reconstruction outcomes. In this paper, we investigate the $\ell_p$ quasi-seminorm, both isotropic and anisotropic $\ell_p$ TV quasi-seminorms, within the framework of the negative binomial statistical model. This problem can be formulated as an optimization problem, which we solve using a gradient-based approach. We present comparisons between the negative binomial and Poisson statistical models using the $\ell_p$ TV quasi-seminorm as well as common penalty terms. Our experimental results highlight the efficacy of the proposed method.
description: 5 pages, Accepted by the IEEE International Symposium on Biomedical Imaging (ISBI)
Elliptic Determinantal Processes and Elliptic Dyson Models
Creators: name: Katori, Makoto
Publisher: name: arXiv
Year: 2017
Subjects: subject: Probability (math.PR)
subject: Statistical Mechanics (cond-mat.stat-mech)
subject: Mathematical Physics (math-ph)
subject: Exactly Solvable and Integrable Systems (nlin.SI)
subject: FOS: Mathematics
subject: FOS: Physical sciences
subject: 60J65, 60G44, 82C22, 60B20, 33E05, 17B22

description: We introduce seven families of stochastic systems of interacting particles in one-dimension corresponding to the seven families of irreducible reduced affine root systems. We prove that they are determinantal in the sense that all spatio-temporal correlation functions are given by determinants controlled by a single function called the spatio-temporal correlation kernel. For the four families ${A}_{N-1}$, ${B}_N$, ${C}_N$ and ${D}_N$, we identify the systems of stochastic differential equations solved by these determinantal processes, which will be regarded as the elliptic extensions of the Dyson model. Here we use the notion of martingales in probability theory and the elliptic determinant evaluations of the Macdonald denominators of irreducible reduced affine root systems given by Rosengren and Schlosser.
Quantum light in curved low dimensional hexagonal boron nitride systems
Creators: name: Chejanovsky, Nathan
name: Kim, Youngwook
name: Zappe, Andrea
name: Stuhlhofer, Benjamin
name: Taniguchi, Takashi
name: Watanabe, Kenji
name: Dasari, Durga Bhaktavatsala Rao
name: Finkler, Amit
name: Smet, Jurgen H.
name: Wrachtrup, Jörg
Publisher: name: arXiv
Year: 2017
Subjects: subject: Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
subject: Materials Science (cond-mat.mtrl-sci)
subject: Quantum Physics (quant-ph)
subject: FOS: Physical sciences

description: Low-dimensional wide bandgap semiconductors open a new playing field in quantum optics using sub-bandgap excitation. In this field, hexagonal boron nitride (h-BN) has been reported to host single quantum emitters (QEs), linking QE density to perimeters. Furthermore, curvature/perimeters in transition metal dichalcogenides (TMDCs) have demonstrated a key role in QE formation. We investigate a curvature-abundant BN system - quasi one-dimensional BN nanotubes (BNNTs) fabricated via a catalyst-free method. We find that non-treated BNNT is an abundant source of stable QEs and analyze their emission features down to single nanotubes, comparing dispersed/suspended material. Combining high spatial resolution of a scanning electron microscope, we categorize and pin-point emission origin to a scale of less than 20 nm, giving us a one-to-one validation of emission source with dimensions smaller than the laser excitation wavelength, elucidating nano-antenna effects. Two emission origins emerge: hybrid/entwined BNNT. By artificially curving h-BN flakes, similar QE spectral features are observed. The impact on emission of solvents used in commercial products and curved regions is also demonstrated. The 'out of the box' availability of QEs in BNNT, lacking processing contamination, is a milestone for unraveling their atomic features. These findings open possibilities for precision engineering of QEs, puts h-BN under a similar 'umbrella' of TMDC's QEs and provides a model explaining QEs spatial localization/formation using electron/ion irradiation and chemical etching.
description: updated abstract
Newton slopes for twisted Artin--Schreier--Witt Towers
Creators: name: Ren, Rufei
Publisher: name: arXiv
Year: 2017
Subjects: subject: Number Theory (math.NT)
subject: FOS: Mathematics

description: We fix a monic polynomial $f(x) \in \mathbb F_q[x]$ over a finite field of characteristic $p$ of degree relatively prime to $p$. Let $a\mapsto ω(a)$ be the Teichmüller lift of $\mathbb F_q$, and let $χ:\mathbb{Z}\to \mathbb C_p^\times$ be a finite character of $\mathbb Z_p$. The $L$-function associated to the polynomial $f$ and the so-called twisted character $ω^u\times χ$ is denoted by $L_f(ω^u,χ,s)$. We prove that, when the conductor of the character is large enough, the $p$-adic Newton slopes of this $L$-function form arithmetic progressions.
Turbulence Strength $C_n^2$ Estimation from Video using Physics-based Deep Learning
Creators: name: Saha, Ripon Kumar
name: Salcin, Esen
name: Kim, Jihoo
name: Smith, Joseph
name: Jayasuriya, Suren
Publisher: name: arXiv
Year: 2024
Subjects: subject: Computer Vision and Pattern Recognition (cs.CV)
subject: Machine Learning (cs.LG)
subject: Image and Video Processing (eess.IV)
subject: FOS: Computer and information sciences
subject: FOS: Electrical engineering, electronic engineering, information engineering

description: Images captured from a long distance suffer from dynamic image distortion due to turbulent flow of air cells with random temperatures, and thus refractive indices. This phenomenon, known as image dancing, is commonly characterized by its refractive-index structure constant $C_n^2$ as a measure of the turbulence strength. For many applications such as atmospheric forecast model, long-range/astronomy imaging, and aviation safety, optical communication technology, $C_n^2$ estimation is critical for accurately sensing the turbulent environment. Previous methods for $C_n^2$ estimation include estimation from meteorological data (temperature, relative humidity, wind shear, etc.) for single-point measurements, two-ended pathlength measurements from optical scintillometer for path-averaged $C_n^2$, and more recently estimating $C_n^2$ from passive video cameras for low cost and hardware complexity. In this paper, we present a comparative analysis of classical image gradient methods for $C_n^2$ estimation and modern deep learning-based methods leveraging convolutional neural networks. To enable this, we collect a dataset of video capture along with reference scintillometer measurements for ground truth, and we release this unique dataset to the scientific community. We observe that deep learning methods can achieve higher accuracy when trained on similar data, but suffer from generalization errors to other, unseen imagery as compared to classical methods. To overcome this trade-off, we present a novel physics-based network architecture that combines learned convolutional layers with a differentiable image gradient method that maintains high accuracy while being generalizable across image datasets.
description: Code Available: https://github.com/Riponcs/Cn2Estimation
Deep Angiogram: Trivializing Retinal Vessel Segmentation
Creators: name: Hu, Dewei
name: Yao, Xing
name: Wang, Jiacheng
name: Tao, Yuankai K.
name: Oguz, Ipek
Publisher: name: arXiv
Year: 2023
Subjects: subject: Image and Video Processing (eess.IV)
subject: Computer Vision and Pattern Recognition (cs.CV)
subject: FOS: Electrical engineering, electronic engineering, information engineering
subject: FOS: Computer and information sciences

description: Among the research efforts to segment the retinal vasculature from fundus images, deep learning models consistently achieve superior performance. However, this data-driven approach is very sensitive to domain shifts. For fundus images, such data distribution changes can easily be caused by variations in illumination conditions as well as the presence of disease-related features such as hemorrhages and drusen. Since the source domain may not include all possible types of pathological cases, a model that can robustly recognize vessels on unseen domains is desirable but remains elusive, despite many proposed segmentation networks of ever-increasing complexity. In this work, we propose a contrastive variational auto-encoder that can filter out irrelevant features and synthesize a latent image, named deep angiogram, representing only the retinal vessels. Then segmentation can be readily accomplished by thresholding the deep angiogram. The generalizability of the synthetic network is improved by the contrastive loss that makes the model less sensitive to variations of image contrast and noisy features. Compared to baseline deep segmentation networks, our model achieves higher segmentation performance via simple thresholding. Our experiments show that the model can generate stable angiograms on different target domains, providing excellent visualization of vessels and a non-invasive, safe alternative to fluorescein angiography.
description: 5 pages, 4 figures, SPIE 2023
Nonviolent unitarization: basic postulates to soft quantum structure of black holes
Creators: name: Giddings, Steven B.
Publisher: name: arXiv
Year: 2017
Subjects: subject: High Energy Physics - Theory (hep-th)
subject: General Relativity and Quantum Cosmology (gr-qc)
subject: FOS: Physical sciences

description: A first-principles approach to the unitarity problem for black holes is systematically explored, based on the postulates of 1) quantum mechanics 2) the ability to approximately locally divide quantum gravitational systems into subsystems 3) correspondence with quantum field theory predictions for appropriate observers and (optionally) 4) universality of new gravitational effects. Unitarity requires interactions between the internal state of a black hole and its surroundings that have not been identified in the field theory description; correspondence with field theory indicates that these are soft. A conjectured information-theoretic result for information transfer between subsystems, partly motivated by a perturbative argument, then constrains the minimum coupling size of these interactions of the quantum atmosphere of a black hole. While large couplings are potentially astronomically observable, given this conjecture one finds that the new couplings can be exponentially small in the black hole entropy, yet achieve the information transfer rate needed for unitarization, due to the large number of black hole internal states. This provides a new possible alternative to arguments for large effects near the horizon. If universality is assumed, these couplings can be described as small, soft, state-dependent fluctuations of the metric near the black hole. Open questions include that of the more fundamental basis for such an effective picture.
description: 31 pages, 1 figure. v2: update to match published version: added ref., minor corrections, brief discussion of relation to previous work
MultiMediate'24: Multi-Domain Engagement Estimation
Creators: name: Müller, Philipp
name: Balazia, Michal
name: Baur, Tobias
name: Dietz, Michael
name: Heimerl, Alexander
name: Penzkofer, Anna
name: Schiller, Dominik
name: Brémond, François
name: Alexandersson, Jan
name: André, Elisabeth
name: Bulling, Andreas
Publisher: name: arXiv
Year: 2024
Subjects: subject: Multimedia (cs.MM)
subject: FOS: Computer and information sciences

description: Estimating the momentary level of participant's engagement is an important prerequisite for assistive systems that support human interactions. Previous work has addressed this task in within-domain evaluation scenarios, i.e. training and testing on the same dataset. This is in contrast to real-life scenarios where domain shifts between training and testing data frequently occur. With MultiMediate'24, we present the first challenge addressing multi-domain engagement estimation. As training data, we utilise the NOXI database of dyadic novice-expert interactions. In addition to within-domain test data, we add two new test domains. First, we introduce recordings following the NOXI protocol but covering languages that are not present in the NOXI training data. Second, we collected novel engagement annotations on the MPIIGroupInteraction dataset which consists of group discussions between three to four people. In this way, MultiMediate'24 evaluates the ability of approaches to generalise across factors such as language and cultural background, group size, task, and screen-mediated vs. face-to-face interaction. This paper describes the MultiMediate'24 challenge and presents baseline results. In addition, we discuss selected challenge solutions.
description: arXiv admin note: text overlap with arXiv:2308.08256
Unusual nanoscale coexistence of polar-nonpolar domains underlying oxygen storage properties in Ho(Mn, Ti)O$_{3+δ}$
Creators: name: Nakajima, Hiroshi
name: Uchihashi, Kento
name: Tsukasaki, Hirofumi
name: Morikawa, Daisuke
name: Tanaka, Hiroyuki
name: Furukawa, Tomohiro
name: Kurushima, Kosuke
name: Yamasaki, Jun
name: Ishibashi, Hiroki
name: Kubota, Yoshiki
name: Sakuda, Atsushi
name: Hayashi, Akitoshi
name: Mori, Shigeo
Publisher: name: arXiv
Year: 2023
Subjects: subject: Materials Science (cond-mat.mtrl-sci)
subject: FOS: Physical sciences

description: Hexagonal manganese oxides RMnO$_3$ show intriguing topological ferroelectric-domain walls with variable conductivity, leading to domain wall engineering. Despite the numerous experimental studies on the polar nanoscale structures, controlling ferroelectric domains has not been sufficiently investigated. Here, we reveal the unprecedented coexistence of polar-nonpolar nanoscale domains that can be formed by substituting Ti ions in HoMnO$_3$. Unusual polar nanoscale domains are embedded in nonpolar domains with different crystallographic symmetry. This polar-nonpolar coexisting structure is naturally assembled by adjusting the lattice length during a solid-state reaction process. Furthermore, the comprehensive study reveals that the reversible microstructural change with a nonpolar-polar transition is strongly correlated with the oxygen storage properties in Ho(Mn, Ti)O$_{3+δ}$. The present results provide important insight into the nanoscale polar-nonpolar domain coexistence in functional rare-earth manganese oxides, RMnO$_3$.