IA Scholar Query: Weakly one-based geometric theories.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgSat, 22 Oct 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Epic Forms with ‑ρο‑
https://scholar.archive.org/work/xr6jnmepojftdojmghu6zxgrya
work_xr6jnmepojftdojmghu6zxgryaSat, 22 Oct 2022 00:00:00 GMTDirectional modulation techniques for secure wireless communication: a comprehensive survey
https://scholar.archive.org/work/6cabjjgtzraxtooqtgkibbio64
AbstractDirectional Modulation (DM) techniques provide wireless communication security against passive eavesdropping by means of specific physical layer characteristics. The original symbol constellations are transmitted along pre-specified spatial direction of legitimate users, while phase-amplitude distorted symbols are transmitted along the undesired directions of eavesdropper. In this paper, a comprehensive review of DM techniques and the most recent developments in this area are discussed. An analysis from three independent Physical Layer Security (PLS) viewpoints; communications, information-theoretic and cryptographic perspective is presented. Different performance metrics in literature are compared and the need for unified PLS approach is emphasized. As DM techniques constitute a relatively new class of PLS, there is no systematic organization of these techniques so far. This paper presents a classification framework for DM comprising of two main categories; angular (1D) and range-angular (2D) techniques. The former secures data along angular direction of physical space, while the latter provides security within certain range (distance) from the transmitter along desired angular direction. Further sub-categorization is based on the under-lying physical layer parameters exploited to achieve security, i.e. space, time, frequency, phase and polarization. The proposed framework is generic, flexible and extend-able to future research. In the end, limitations of existing techniques are pointed out and research directions are suggested.Omar Ansari, Muhammad Aminwork_6cabjjgtzraxtooqtgkibbio64Sat, 24 Sep 2022 00:00:00 GMTExploiting the "Lego brick" approach to predict accurate molecular structures of PAHs and PANHs
https://scholar.archive.org/work/6jez2i7pw5h2be6a5cxmtxp674
Polycyclic aromatic hydrocarbons (PAHs) and polycyclic aromatic nitrogen heterocycles (PANHs) are important and ubiquitous species in space. However, their accurate structural and spectroscopic characterization is often missing. To fill this...Hexu Ye, Silvia Alessandrini, Mattia Melosso, Cristina Puzzariniwork_6jez2i7pw5h2be6a5cxmtxp674Fri, 23 Sep 2022 00:00:00 GMTThe role of crystal facets and disorder on photo-electrosynthesis
https://scholar.archive.org/work/23x6kalm4bafvcaacjpcwz3diy
Photoelectrochemistry has the potential to play a crucial role in the storage of solar energy and the realisation of a circular economy. From a chemical viewpoint, achieving high conversion efficiencies requires subtle control of the catalyst surface and its interaction with the electrolyte. Traditionally, such control has been hard to achieve in the complex multinary oxides used in PEC devices and consequently the mechanisms by which surface exposed facets influence light-driven catalysts are poorly understood. Yet, this understanding is critical to further improve conversion yields and fine-tune reaction selectivities. Here, we review the impact that crystal facets and disorder have on photoelectrochemical reactivity. In particular, we discuss how the crystal orientation influences the energetics of the surface, the existence of defects and the transport of reactive charges, ultimately dictating the PEC activity. Moreover, we evaluate how facet stability dictates the tendency of the solid to undergo reconstructions during catalytic processes and highlight the experimental and computational challenges that must be overcome to characterise the role of the exposed facets and disorder in catalytic performance.Ernest Pastor, Laura Montañés, Ana Gutiérrez-Blanco, Franziska S Hegner, Camilo A Mesa, Núria López, Sixto Giménezwork_23x6kalm4bafvcaacjpcwz3diyFri, 23 Sep 2022 00:00:00 GMTStable singularity formation for the Keller-Segel system in three dimensions
https://scholar.archive.org/work/jmnqkt6p6nge5po2abaqs2lue4
We consider the parabolic-elliptic Keller-Segel system in dimensions d ≥ 3, which is the mass supercritical case. This system is known to exhibit rich dynamical behavior including singularity formation via self-similar solutions. An explicit example has been found more than two decades ago by Brenner et al. , and is conjectured to be nonlinearly radially stable. We prove this conjecture for d=3. Our approach consists of reformulating the problem in similarity variables and studying the Cauchy evolution in intersection Sobolev spaces via semigroup theory methods. To solve the underlying spectral problem, we crucially rely on a technique we recently developed in . To our knowledge, this provides the first result on stable self-similar blowup for the Keller-Segel system. Furthermore, the extension of our result to any higher dimension is straightforward. We point out that our approach is general and robust, and can therefore be applied to a wide class of parabolic models.Irfan Glogić, Birgit Schörkhuberwork_jmnqkt6p6nge5po2abaqs2lue4Thu, 22 Sep 2022 00:00:00 GMTA strong characterization of the entries of the Burau matrices of 4-braids: The Burau representation of the braid group B_4 is faithful almost everywhere
https://scholar.archive.org/work/avdgiqlpyzgmxg66op2o55tvdu
We establish strong constraints on the kernel of the (reduced) Burau representation β_4:B_4→GL_3(ℤ[q^± 1]) of the braid group B_4. We develop a theory to explicitly determine the entries of the Burau matrices of braids in B_4, and this is an important step toward demonstrating that β_4 is faithful (a longstanding question posed in the 1930s). The theory is based on a novel combinatorial interpretation of β_4(g), in terms of the Garside normal form of g∈ B_4 and a new product decomposition of positive braids. We develop cancellation results for words in matrix groups to show that if σ is a generic positive braid in B_4 and if t≠ 2 is a prime number, then the leading coefficients in at least one row of the matrix β_4(σ) are non-zero modulo t. We exploit these cancellation results to deduce that the Burau representation of B_4 is faithful almost everywhere.Amitesh Dattawork_avdgiqlpyzgmxg66op2o55tvduThu, 22 Sep 2022 00:00:00 GMTSome branching laws for symmetric spaces
https://scholar.archive.org/work/b4vzhhmvmfhrxk2ni3yenphloa
In this paper we consider the unitary symmetric spaces of the form X=U(p,q)/U(1)U(p,q-1) and their discrete series representations. Inspired by the work of A.Venkatesh and Y.Sekellarides on L-groups of p-adic spherical spaces we formulate and prove natural relative branching laws for the restriction to smaller subgroups of the same type and corresponding unitary spaces.We think of this as steps to formulation and proving Gan Gross Prasad conjectures for unitary spaces. Using period integral and some results of T.Kobayashi we prove an analogue of thesis conjectures.Bent Orsted, Birgit Spehwork_b4vzhhmvmfhrxk2ni3yenphloaThu, 22 Sep 2022 00:00:00 GMTLévy flights as an emergent phenomenon in a spatially extended system
https://scholar.archive.org/work/kmahxkvt2vgxpnp7garuugsqyy
We provide an example of a stochastic partial differential equation (SPDE) which, despite only driven by Gaussian white noise, exhibits superdiffusive behaviour. The anomalous diffusion is an entirely emergent behaviour and manifests itself in jumps in the location of a travelling front solution. Using a collective coordinate approach we reduce the SPDE to a set of stochastic differential equations (SDEs) driven by Gaussian white noise. This allows us to identify the mechanism giving rise to the anomalous diffusion: We find that the emergence of anomalous diffusion is induced by random widening events of the front interface.Chunxi Jiao, Georg A. Gottwaldwork_kmahxkvt2vgxpnp7garuugsqyyThu, 22 Sep 2022 00:00:00 GMTHurwitz numbers for reflection groups II: Parabolic quasi-Coxeter elements
https://scholar.archive.org/work/glpyk7qqivcbnibclqlfhmkbyq
We define parabolic quasi-Coxeter elements in well generated complex reflection groups. We characterize them in multiple natural ways, and we study two combinatorial objects associated with them: the collections Red_W(g) of reduced reflection factorizations of g and RGS(W,g) of the relative generating sets of g. We compute the cardinalities of these sets for large families of parabolic quasi-Coxeter elements and, in particular, we relate the size #Red_W(g) with geometric invariants of Frobenius manifolds. This paper is second in a series of three; we will rely on many of its results in part III to prove uniform formulas that enumerate full reflection factorizations of parabolic quasi-Coxeter elements, generalizing the genus-0 Hurwitz numbers.Theo Douvropoulos, Joel Brewster Lewis, Alejandro H. Moraleswork_glpyk7qqivcbnibclqlfhmkbyqThu, 22 Sep 2022 00:00:00 GMTTame parahoric nonabelian Hodge correspondence on curves
https://scholar.archive.org/work/upwtjfbvcjf57jz74jslk7zeci
The nonabelian Hodge correspondence for vector bundles over noncompact curves is adequately described by implementing a weighted filtration on the objects involved. In order to establish a full correspondence between a Dolbeault and a de Rham space for a general complex reductive group G, we introduce torsors given by parahoric group schemes in the sense of Bruhat–Tits. Combined with existing results on the Riemann–Hilbert correspondence for logarithmic parahoric connections, this gives a full nonabelian Hodge correspondence from Higgs bundles to fundamental group representations over a noncompact curve beyond the GL_n(ℂ)-case.Pengfei Huang, Georgios Kydonakis, Hao Sun, Lutian Zhaowork_upwtjfbvcjf57jz74jslk7zeciThu, 22 Sep 2022 00:00:00 GMTTowards testing the Fröhlich-Morchio-Strocchi mechanism in quantum gravity
https://scholar.archive.org/work/agyegzdftncbdpkitzidu5nviu
Physics in (canonical) quantum gravity needs to be manifestly diffeomorphism-invariant. Consequently, physical observables need to be formulated in terms of manifestly diffeomorphism-invariant operators, which are necessarily composite. This makes an evaluation in general involved, even if the concrete implementation of quantum gravity should be treatable (semi-)perturbatively in general. A mechanism developed by Fr\"ohlich, Morchio and Strocchi for flat-space-time quantum field theory may also be applicable in this case. It may be possible to test this mechanism with methods like dynamical triangulation.Axel Maaswork_agyegzdftncbdpkitzidu5nviuThu, 22 Sep 2022 00:00:00 GMTMatter-antimatter asymmetry restrains the dimensionality of neural representations: quantum decryption of large-scale neural coding
https://scholar.archive.org/work/owy6xa2v3bcx3muopa5kiug5hm
Projections from the study of the human universe onto the study of the self-organizing brain are herein leveraged to address certain concerns raised in latest neuroscience research, namely (i) the extent to which neural codes are multidimensional; (ii) the functional role of neural dark matter; (iii) the challenge to traditional model frameworks posed by the needs for accurate interpretation of large-scale neural recordings linking brain and behavior. On the grounds of (hyper-)self-duality under (hyper-)mirror supersymmetry, inter-relativistic principles are introduced, whose consolidation, as spin-geometrical pillars of a network- and game-theoretical construction, is conducive to (i) the high-precision reproduction of core experimental observations on neural coding in the self-organizing brain, whereby the instantaneous geometric dimensionality of neural representations of a spontaneous behavioral state is proven to be at most 16, unidirectionally; (ii) spinor (co-)representations, as the latent building blocks of self-organizing cortical circuits subserving (co-)behavioral states; (iii) an early crystallization of pertinent multidimensional synaptic (co-)architectures, whereby Lorentz (co-)partitions are in principle verifiable; and, ultimately, (iv) potentially inverse insights into matter-antimatter asymmetry. New avenues for the decryption of large-scale neural coding in health and disease are being discussed.Sofia Karamintziouwork_owy6xa2v3bcx3muopa5kiug5hmThu, 22 Sep 2022 00:00:00 GMTSharply o-minimal structures and sharp cellular decomposition
https://scholar.archive.org/work/ws56jyagzraklhkas5uouwtvgm
Sharply o-minimal structures (denoted -minimal) are a strict subclass of the o-minimal structures, aimed at capturing some finer features of structures arising from algebraic geometry and Hodge theory. Sharp o-minimality associates to each definable set a pair of integers known as format and degree, similar to the ambient dimension and degree in the algebraic case; gives bounds on the growth of these quantities under the logical operations; and allows one to control the geometric complexity of a set in terms of its format and degree. These axioms have significant implications on arithmetic properties of definable sets – for example, -minimality was recently used by the authors to settle Wilkie's conjecture on rational points in ℝ_exp-definable sets. In this paper we develop some basic theory of sharply o-minimal structures. We introduce the notions of reduction and equivalence on the class of -minimal structures. We give three variants of the definition of -minimality, of increasing strength, and show that they all agree up to reduction. We also consider the problem of "sharp cell decomposition", i.e. cell decomposition with good control on the number of the cells and their formats and degrees. We show that every -minimal structure can be reduced to one admitting sharp cell decomposition, and use this to prove bounds on the Betti numbers of definable sets in terms of format and degree.Gal Binyamini, Dmitri Novikov, Benny Zackwork_ws56jyagzraklhkas5uouwtvgmThu, 22 Sep 2022 00:00:00 GMTIntroduction to topological defects: from liquid crystals to particle physics
https://scholar.archive.org/work/4hjm4qjjkveypj3jh6sj4mxo2u
Liquid crystals are assemblies of rod-like molecules which self-organize to form mesophases, in-between ordinary liquids and anisotropic crystals. At each point, the molecules collectively orient themselves along a privileged direction, which locally defines an orientational order. Sometimes, this order is broken and singularities appear in the form of topological defects. This tutorial article is dedicated to the geometry, topology and physics of these defects. We introduce the main models used to describe the nematic phase and discuss the isotropic-nematic phase transition. Then, we present the different families of defects in nematics and examine some of their physical outcomes. Finally, we show that topological defects are universal patterns of nature, appearing not only in soft matter, but also in biology, cosmology, geology and even particle physics.Sébastien Fumeron, Bertrand Berchework_4hjm4qjjkveypj3jh6sj4mxo2uThu, 22 Sep 2022 00:00:00 GMTThe Branes Behind Generalized Symmetry Operators
https://scholar.archive.org/work/yaux262fkfavvkigxfiwkyzoxy
The modern approach to m-form global symmetries in a d-dimensional quantum field theory (QFT) entails specifying dimension d-m-1 topological generalized symmetry operators which non-trivially link with m-dimensional defect operators. In QFTs engineered via string constructions on a non-compact geometry X, these defects descend from branes wrapped on non-compact cycles which extend from a localized source / singularity to the boundary ∂ X. The generalized symmetry operators which link with these defects arise from magnetic dual branes wrapped on cycles in ∂ X. This provides a systematic way to read off various properties of such topological operators, including their worldvolume topological field theories, and the resulting fusion rules. We illustrate these general features in the context of 6D superconformal field theories, where we use the F-theory realization of these theories to read off the worldvolume theory on the generalized symmetry operators. Defects of dimension 3 which are charged under a suitable 3-form symmetry detect a non-invertible fusion rule for these operators. We also sketch how similar considerations hold for related systems.Jonathan J. Heckman, Max Hübner, Ethan Torres, Hao Y. Zhangwork_yaux262fkfavvkigxfiwkyzoxyThu, 22 Sep 2022 00:00:00 GMTAsymptotics of finite energy monopoles on AC 3-manifolds
https://scholar.archive.org/work/u4omm5qntbhh5crdqbuzzntrea
We study the asymptotic behavior of finite energy SU(2) monopoles, and general critical points of the SU(2) Yang–Mills–Higgs energy, on asymptotically conical 3-manifolds with only one end. Our main results generalize classical results due to Groisser and Taubes in the particular case of the flat 3-dimensional Euclidean space ℝ^3. Indeed, we prove the integrality of the monopole number, or charge, of finite energy configurations, and derive the classical energy formula establishing monopoles as absolute minima. Moreover, we prove that the covariant derivative of the Higgs field of a critical point of the energy decays quadratically along the end, and that its transverse component with respect to the Higgs field, as well as the corresponding component of the curvature of the underlying connection, actually decay exponentially. Additionally, under the assumption of positive Gaussian curvature on the asymptotic link, we prove that the curvature of any critical point connection decays quadratically. Furthermore, we deduce that any irreducible critical point converges uniformly along the conical end to a limiting configuration at infinity consisting of a reducible Yang–Mills connection and a parallel Higgs field.Daniel Fadelwork_u4omm5qntbhh5crdqbuzzntreaThu, 22 Sep 2022 00:00:00 GMTUnlikely Intersections with Bruhat Strata
https://scholar.archive.org/work/hqectgs3dzet7orrkwzurzbvsq
Let 𝒜_g be the moduli space of g-dimensional principally polarized abelian varieties over ℤ, and let 𝒯⊂𝒜_g be a closed locus, also defined over ℤ. Motivated by unlikely intersection conjectures, we study the intersection of 𝒯_𝔽_p with the Bruhat strata in 𝒜_g,𝔽_p as p-varies; these are strata characterized by the existence of certain subgroup schemes inside the p-torsion of the fibres. We find that, away from a finite set of primes, positive-dimensional "unlikely" intersections of 𝒯_𝔽_p with such strata are all accounted for by intersections of 𝒯 with special loci inside 𝒜_g. This result generalizes to all abelian-type Shimura varieties, and variations of Hodge structures equipped with certain motivic data. It moreover gives another example of how functional transcendence principles in characteristic zero can be used to study unlikely intersections in positive characteristic, building on recent work by the author.David Urbanikwork_hqectgs3dzet7orrkwzurzbvsqThu, 22 Sep 2022 00:00:00 GMTGlobal attraction and repulsion of a heteroclinic limit cycle in three dimensional Kolmogorov maps
https://scholar.archive.org/work/ifwtmjqdtjexpiahysfyjyzqqe
There is a recent development in the carrying simplex theory for competitive maps: under some weaker conditions a map has a modified carrying simplex (one of the author's latest publications). In this paper, as one of the applications of the modified carrying simplex theory, a criterion is established for a three dimensional Kolmogorov map to have a globally repelling (attracting) heteroclinic limit cycle. As a concrete example, a discrete competitive model is investigated to illustrate the above criteria for global repulsion (attraction) of a hetericlinic limit cycle.Zhanyuan Houwork_ifwtmjqdtjexpiahysfyjyzqqeThu, 22 Sep 2022 00:00:00 GMTOn the convex formulations of robust Markov decision processes
https://scholar.archive.org/work/plob7n5zuzdmppkt7rfy3o2o5i
Robust Markov decision processes (MDPs) are used for applications of dynamic optimization in uncertain environments and have been studied extensively. Many of the main properties and algorithms of MDPs, such as value iteration and policy iteration, extend directly to RMDPs. Surprisingly, there is no known analog of the MDP convex optimization formulation for solving RMDPs. This work describes the first convex optimization formulation of RMDPs under the classical sa-rectangularity and s-rectangularity assumptions. We derive a convex formulation with a linear number of variables and constraints but large coefficients in the constraints by using entropic regularization and exponential change of variables. Our formulation can be combined with efficient methods from convex optimization to obtain new algorithms for solving RMDPs with uncertain probabilities. We further simplify the formulation for RMDPs with polyhedral uncertainty sets. Our work opens a new research direction for RMDPs and can serve as a first step toward obtaining a tractable convex formulation of RMDPs.Julien Grand-Clément, Marek Petrikwork_plob7n5zuzdmppkt7rfy3o2o5iWed, 21 Sep 2022 00:00:00 GMTJet thermalization in QCD kinetic theory
https://scholar.archive.org/work/rt5ux5vfpzd7hedtrqighx4rsy
We perform numerical studies in QCD kinetic theory to investigate the energy and angular profiles of a high energy parton - as a proxy for a jet produced heavy ion collisions - passing through a Quark-Gluon Plasma (QGP). We find that the fast parton loses energy to the plasma mainly via a radiative turbulent gluon cascade that transport energy locally from the jet down to the temperature scale where dissipation takes place. In this first stage, the angular structure of the turbulent cascade is found to be relatively collimated. However, when the lost energy reaches the plasma temperature is it rapidly transported to large angles w.r.t. the jet axis and thermalizes. We investigate the contribution of the soft jet constituents to the total jet energy. We show that for jet opening angles of about 0.3 rad or smaller the effect is negligible. Conversely, larger opening angles become more and more sensitive to the thermal component of the jet and thus to medium response. Our result showcase the importance of the jet cone size in mitigating or enhancing the details of dissipation in jet quenching observables.Y. Mehtar-Tani, S. Schlichting, I. Soudiwork_rt5ux5vfpzd7hedtrqighx4rsyWed, 21 Sep 2022 00:00:00 GMT