搜索结果：Theory in biosciences = Theorie in den Biowissenschaften

This work concentrates on the study of inverse determinant sums, which arise from the union bound on the error probability, as a tool for designing and analyzing algebraic space-time block codes. A general framework to study these sums is established, and the connection between asymptotic growth of inverse determinant sums and the diversity-multiplexing gain trade-off is investigated. It is proven that the growth of the inverse determinant sum of a division algebra-based space-time code is completely determined by the growth of the unit group. This reduces the inverse determinant sum analysis to studying certain asymptotic integrals in Lie groups. Using recent methods from ergodic theory, a complete classification of the inverse determinant sums of the most well known algebraic space-time codes is provided. The approach reveals an interesting and tight relation between diversity-multiplexing gain trade-off and point counting in Lie groups.

In a series of recent works based on foliation-based quantization in which renormalizability has been achieved for the physical sector of the theory, we have shown that the use of the standard graviton propagator interferes, due to the presence of the trace mode, with the 4D covariance. A subtlety in the background field method also requires careful handling. This status of the matter motivated us to revisit an Einstein-scalar system in one of the sequels. Continuing the endeavors, we revisit the one-loop renormalization of an Einstein-Maxwell system in the present work. The systematic renormalization of the cosmological and Newton's constants is carried out by applying the refined background field method. One-loop beta function of the vector coupling constant is explicitly computed and compared with the literature. The longstanding problem of gauge choice-dependence of the effective action is addressed and the manner in which the gauge-choice independence is restored in the present framework is discussed. The formalism also sheds light on background independent analysis. The renormalization involves a metric field redefinition originally introduced by `t Hooft; with the field rede

Pattern languages are a classical model in formal language theory and algorithmic learning theory. This note formulates the problem of computing the inclusion depth of a pattern language: the length of the longest strict inclusion chain from the universal pattern language to the language generated by a given pattern. Inclusion depth captures the mind-change complexity of pattern identification from positive data. The central open question is whether the inclusion depth ID_Sigma(p) is computable for every pattern p over every finite alphabet Sigma with at least two symbols, and whether it is computable in polynomial time. A simple conjectured formula, ID_Sigma(p) = 2|p| - #var(p) - 1, would imply a linear-time algorithm. The problem connects pattern language inclusion, combinatorics on words, language identification in the limit, and mind-change-bounded learning.

Canonical formulation of quantum field theory on the Light Front (LF) is reviewed. The problem of constructing the LF Hamiltonian which gives the theory equivalent to original Lorentz and gauge invariant one is considered. We describe possible ways of solving this problem: (a) the limiting transition from the equal-time Hamiltonian in a fastly moving Lorentz frame to LF Hamiltonian, (b) the direct comparison of LF perturbation theory in coupling constant and usual Lorentz-covariant Feynman perturbation theory. Gauge invariant regularization of LF Hamiltonian via introducing a lattice in transverse coordinates and imposing periodic boundary conditions in LF coordinate $x^-$ for gauge fields on the interval $|x^-|< L$ is considered. We find that LF canonical formalism for this regularization avoid usual most complicated constraints connecting zero and nonzero modes of gauge fields.

In a previous paper, we showed nonvaninishing of the universal index elements in the K-theory of the maximal C*-algebras of the fundamental groups of enlargeable spin manifolds. The underlying notion of enlargeability was the one from the first relevant paper of Gromov and Lawson, involving contracting maps defined on finite covers of the given manifolds. In the paper at hand, we weaken this assumption to the one in the second paper of Gromov and Lawson, where infinite covers are allowed. The new idea is the construction of a geometrically given C*-algebra with trace which encodes the information given by these infinite covers; along the way we obtain an easy proof of a relative index theorem relevant in this context.

We present a foliation-focused critical review of the boundary conditions and dynamics of 4D gravitational theories. A general coordinate transformation introduces a new foliation and changes the hypersurface on which a natural boundary condition is imposed; in this sense gauge transformations must be viewed as changing the boundary conditions. The issue of a gauge invariant boundary condition is nontrivial and has been extensively studied in the literature. We turn around the difficulty in obtaining such a boundary condition (and subtleties observed in the main body) and take it as one of the indications of an enlarged Hilbert space so as to include the states satisfying different boundary conditions. Through the systematical reduction procedure we obtain, up to some peculiarities, the explicit form of the reduced Lagrangian that describes the dynamics of the physical states. We examine the new insights offered by the 3D Lagrangian on BMS-type symmetry and black hole information. In particular we confirm that the boundary dynamics is an indispensable part of the system information.

The BKR inequality conjectured by van den Berg and Kesten in [11], and proved by Reimer in [8], states that for $A$ and $B$ events on $S$, a finite product of finite sets $S_i,i=1,\ldots,n$, and $P$ any product measure on $S$, $$ P(A \Box B) \le P(A)P(B),$$ where the set $A \Box B$ consists of the elementary events which lie in both $A$ and $B$ for `disjoint reasons.' Precisely, with ${\bf n}:=\{1,\ldots,n\}$ and $K \subset {\bf n}$, for ${\bf x} \in S$ letting $[{\bf x}]_K=\{{\bf y} \in S: y_i = x_i, i \in K\}$, the set $A \Box B$ consists of all ${\bf x} \in S$ for which there exist disjoint subsets $K$ and $L$ of ${\bf n}$ for which $[{\bf x}]_K \subset A$ and $[{\bf x}]_L \subset B$. The BKR inequality is extended to the following functional version on a general finite product measure space $(S,\mathbb{S})$ with product probability measure $P$, $$E\left\{ \max_{\stackrel{K \cap L = \emptyset}{K \subset {\bf n}, L \subset {\bf n}}} \underline{f}_K({\bf X})\underline{g}_L({\bf X})\right\} \leq E\left\{f({\bf X})\right\}\,E\left\{g({\bf X})\right\},$$ where $f$ and $g$ are non-negative measurable functions, $\underline{f}_K({\bf x}) = {\rm ess} \inf_{{\bf y} \in [{\bf x}]_K}f({\bf

An open problem in polarization theory is to determine the binary operations that always lead to polarization (in the general multilevel sense) when they are used in Arıkan style constructions. This paper, which is presented in two parts, solves this problem by providing a necessary and sufficient condition for a binary operation to be polarizing. This (first) part of the paper introduces the mathematical framework that we will use in the second part to characterize the polarizing operations. We define uniformity preserving, irreducible, ergodic and strongly ergodic operations and we study their properties. The concepts of a stable partition and the residue of a stable partition are introduced. We show that an ergodic operation is strongly ergodic if and only if all its stable partitions are their own residues. We also study the products of binary operations and the structure of their stable partitions. We show that the product of a sequence of binary operations is strongly ergodic if and only if all the operations in the sequence are strongly ergodic. In the second part of the paper, we provide a foundation of polarization theory based on the ergodic theory of binary operations th

The location of the neutron drip line, currently known for only the lightest elements, remains a fundamental question in nuclear physics. Its description is a challenge for microscopic nuclear energy density functionals, as it must take into account in a realistic way not only the nuclear potential, but also pairing correlations, deformation effects and coupling to the continuum. The recently developed deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) aims to provide a unified description of even-even nuclei throughout the nuclear chart. Here, the DRHBc with the successful density functional PC-PK1 is used to investigate whether and how deformation influences the prediction for the neutron drip-line location for even-even nuclei with 8<=Z<=20, where many isotopes are predicted deformed. The results are compared with those based on the spherical relativistic continuum Hartree-Bogoliubov (RCHB) theory and discussed in terms of shape evolution and the variational principle. It is found that the Ne and Ar drip-line nuclei are different after the deformation effect is included. The direction of the change is not necessarily towards an extended drip line, but rat

Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. We focus on a single locus, any number of alleles in a two-gender dioecious population, for a large class of systems within population genetics. Our governing equations are time-dependent differential equations labeled by a set of genotype frequencies. Our equations are uniquely derived from 4 assumptions within any population: (1) a closed system; (2) average-and-random mating process (mean-field behavior); (3) Mendelian inheritance; (4) exponential growth/death. Although our equations are nonlinear with time-evolutionary dynamics, we have obtained an exact analytic time-dependent solution and an exactly solvable model. From the phenomenological viewpoint, any initial parameter of genotype frequencies of a closed system will eventually approach a stable fixed point. Under time evolution, we show (1) the monotonic behavior of genotype frequencies, (2) any genotype or allele that appears in the population will never become extinct, (3) the Hardy-Weinberg law, and (4) the global stability without chaos in the parameter space. To demonstrate the experimental evidence for our theory, as an

We survey some of the AGT relations between N=2 gauge theories in four dimensions and geometric representations of symmetry algebras of two-dimensional conformal field theory on the equivariant cohomology of their instanton moduli spaces. We treat the cases of gauge theories on both flat space and ALE spaces in some detail, and with emphasis on the implications arising from embedding them into supersymmetric theories in six dimensions. Along the way we construct new toric noncommutative ALE spaces using the general theory of complex algebraic deformations of toric varieties, and indicate how to generalise the construction of instanton moduli spaces. We also compute the equivariant partition functions of topologically twisted six-dimensional Yang-Mills theory with maximal supersymmetry in a general Omega-background, and use the construction to obtain novel reductions to theories in four dimensions.

An open problem in polarization theory is to determine the binary operations that always lead to polarization (in the general multilevel sense) when they are used in Arıkan style constructions. This paper, which is presented in two parts, solves this problem by providing a necessary and sufficient condition for a binary operation to be polarizing. This (second) part provides a foundation of polarization theory based on the ergodic theory of binary operations which we developed in the first part. We show that a binary operation is polarizing if and only if it is uniformity preserving and its right-inverse is strongly ergodic. The rate of polarization of single user channels is studied. It is shown that the exponent of any polarizing operation cannot exceed $\frac{1}{2}$, which is the exponent of quasigroup operations. We also study the polarization of multiple access channels (MAC). In particular, we show that a sequence of binary operations is MAC-polarizing if and only if each binary operation in the sequence is polarizing. It is shown that the exponent of any MAC-polarizing sequence cannot exceed $\frac{1}{2}$, which is the exponent of sequences of quasigroup operations.

Involutive category theory provides a flexible framework to describe involutive structures on algebraic objects, such as anti-linear involutions on complex vector spaces. Motivated by the prominent role of involutions in quantum (field) theory, we develop the involutive analogs of colored operads and their algebras, named colored $\ast$-operads and $\ast$-algebras. Central to the definition of colored $\ast$-operads is the involutive monoidal category of symmetric sequences, which we obtain from a general product-exponential $2$-adjunction whose right adjoint forms involutive functor categories. For $\ast$-algebras over $\ast$-operads we obtain involutive analogs of the usual change of color and operad adjunctions. As an application, we turn the colored operads for algebraic quantum field theory into colored $\ast$-operads. The simplest instance is the associative $\ast$-operad, whose $\ast$-algebras are unital and associative $\ast$-algebras.

The assignment (nonstable K_0-theory), that to a ring R associates the monoid V(R) of Murray-von Neumann equivalence classes of idempotent infinite matrices with only finitely nonzero entries over R, extends naturally to a functor. We prove the following lifting properties of that functor: (1) There is no functor F, from simplicial monoids with order-unit with normalized positive homomorphisms to exchange rings, such that VF is equivalent to the identity. (2) There is no functor F, from simplicial monoids with order-unit with normalized positive embeddings to C*-algebras of real rank 0 (resp., von Neumann regular rings), such that VF is equivalent to the identity. (3) There is a {0,1}^3-indexed commutative diagram D of simplicial monoids that can be lifted, with respect to the functor V, by exchange rings and by C*-algebras of real rank 1, but not by semiprimitive exchange rings, thus neither by regular rings nor by C*-algebras of real rank 0. By using categorical tools from an earlier paper (larders, lifters, CLL), we deduce that there exists a unital exchange ring of cardinality aleph three (resp., an aleph three-separable unital C*-algebra of real rank 1) R, with stable rank 1 a

Shape coexistence in even-even nuclei is observed when the ground state band of a nucleus is accompanied by another K=0 band at similar energy but with radically different structure. We attempt to predict regions of shape coexistence throughout the nuclear chart using the parameter-free proxy-SU(3) symmetry and standard covariant density functional theory. Within the proxy-SU(3) symmetry the interplay of shell model magic numbers, formed by the spin-orbit interaction, and the 3-dimensional isotropic harmonic oscillator magic numbers, leads to the prediction of specific horizontal and vertical stripes on the nuclear chart in which shape coexistence should be possible. Within covariant density functional theory, specific islands on the nuclear chart are found, in which particle-hole excitations leading to shape coexistence are observed. The role played by particle-hole excitations across magic numbers as well as the collapse of magic numbers as deformation sets in is clarified.

The elastic p-12C scattering at low energies is studied by using a cluster effective field theory (EFT), where the low-lying resonance states (s1/2, p3/2, d5/2) of 13N are treated as pertinent degrees of freedom. The low-energy constants of the Lagrangian are expressed in terms of the Coulomb-modified effective range parameters, which are determined to reproduce the experimental data for the differential cross-sections. The resulting theoretical predictions agree very well with the experimental data. The resulting theory is shown to give us almost identical phase shifts as obtained from the R-matrix approach. The role of the ground state of 13N below the threshold and the next-to-leading order in the EFT power counting are also discussed.

Despite recent advances in text-conditioned 3D indoor scene generation, there remain gaps in the evaluation of these methods. Existing metrics often measure realism by comparing generated scenes to a set of ground-truth scenes, but they overlook how well scenes follow the input text and capture implicit expectations of plausibility. We present SceneEval, an evaluation framework designed to address these limitations. SceneEval introduces fine-grained metrics for explicit user requirements-including object counts, attributes, and spatial relationships-and complementary metrics for implicit expectations such as support, collisions, and navigability. Together, these provide interpretable and comprehensive assessments of scene quality. To ground evaluation, we curate SceneEval-500, a benchmark of 500 text descriptions with detailed annotations of expected scene properties. This dataset establishes a common reference for reproducible and systematic comparison across scene generation methods. We evaluate six recent scene generation approaches using SceneEval and demonstrate its ability to provide detailed assessments of the generated scenes, highlighting strengths and areas for improvemen

The Jupiter-Saturn 2:5 near-commensurability is analyzed in a fully analytic Hamiltonian planetary theory. Computations for the Sun-Jupiter-Saturn system, extending to the third order of the masses and to the 8th degree in the eccentricities and inclinations, reveal an unexpectedly sensitive dependence of the solution on initial data and its likely nonconvergence. The source of the sensitivity and apparent lack of convergence is this near-commensurability, the so-called great inequality. This indicates that simple averaging, still common in current semi-analytic planetary theories, may not be an adequate technique to obtain information on the long-term dynamics of the Solar System. Preliminary results suggest that these difficulties can be overcome by using resonant normal forms.

In this paper we deal with Grothendieck's interpretation of Artin's interpretation of Galois's Galois Theory (and its natural relation with the fundamental group and the theory of coverings) as he developed it in Expose V, section 4, ``Conditions axiomatiques d'une theorie de Galois'' in the SGA1 1960/61. This is a beautiful piece of mathematics very rich in categorical concepts, and goes much beyond the original Galois's scope (just as Galois went much further than the non resubility of the quintic equation). We show explicitly how Grothendieck's abstraction corresponds to Galois work. We introduce some axioms and prove a theorem of characterization of the category (topos) of actions of a discrete group. This theorem corresponds exactly to Galois fundamental result. The theorem of Grothendieck characterizes the category (topos) of continuous actions of a profinite topological group. We develop a proof of this result as a "passage into the limit'' (in an inverse limit of topoi) of our theorem of characterization of the topos of actions of a discrete group. We deal with the inverse limit of topoi just working with an ordinary filtered colimit (or union) of the small categories which