Miracle-dz/UniFAR-FTUs huggingface dataset:
Framed transfers and motivic fundamental classes

We relate the recognition principle for infinite P1 ‐loop spaces to the theory of motivic fundamental classes of Déglise, Jin and Khan. We first compare two kinds of transfers that are naturally defined on cohomology theories represented by motivic spectra: the framed transfers given by the recognition principle, which arise from Voevodsky's computation of the Nisnevish sheaf associated with An/(An−0) , and the Gysin transfers defined via Verdier's deformation to the normal cone. We then introduce the category of finite R ‐correspondences for R a motivic ring spectrum, generalizing Voevodsky's category of finite correspondences and Calmès and Fasel's category of finite Milnor–Witt correspondences. Using the formalism of fundamental classes, we show that the natural functor from the category of framed correspondences to the category of R ‐module spectra factors through the category of finite R ‐correspondences.
Cash‐Flow Based Dynamic Inventory Management

Small‐to‐medium‐sized enterprises (SMEs), including many startup firms, need to manage interrelated flows of cash and inventories of goods. In this study, we model a firm that can finance its inventory (ordered or manufactured) with loans in order to meet random demand which in general may not be time stationary. The firm earns interest on its cash on hand and pays interest on its debt. The objective is to maximize the expected value of the firm's capital at the end of a finite planning horizon. The firm's state at the beginning of each period is characterized by the inventory level and the capital level measured in units of the product, whose sum represents the “net worth” of the firm. Our study shows that the optimal ordering policy is characterized by a pair of threshold parameters as follows. (i) If the net worth is less than the lower threshold, then the firm employs a base stock order up to the lower threshold. (ii) If the net worth is between the two thresholds, then the firm orders exactly as many units as it can afford, without borrowing. (iii) If the net worth is above the upper threshold, then the firm employs a base stock order up to the upper threshold. Further, upper and lower bounds for the threshold values are developed using two simple‐to‐compute myopic ordering policies which yield lower bounds for the value function. We also derive an upper bound for the value function by considering a sell‐back policy. Subsequently, it is shown that policies of similar structure are optimal when the loan and deposit interest rates are piecewise linear functions, when there is a maximal loan limit and when unsatisfied demand is backordered. Finally, further managerial insights are provided with extensive numerical studies.
PRIMITIVE PERMUTATION GROUPS CONTAINING A CYCLE

Abstract The primitive finite permutation groups containing a cycle are classified. Of these, only the alternating and symmetric groups contain a cycle fixing at least three points. This removes a primality condition from a classical theorem of Jordan. Some applications to monodromy groups are given, and the contributions of Jordan and Marggraff to this topic are briefly discussed.
Convolutions on the Haagerup tensor products of Fourier algebras

We study the ranges of the maps of convolution $u\otimes v\mapsto u\ast v$ and a `twisted' convolution $u\otimes v\mapsto u\ast \check{v}$ ($\check{u}(s)=u(s^{-1})$) and on the Haagerup tensor product of a Fourier algebra of a compact group $A(G)$ with itself. We compare the results to result of factoring these maps through projective and operator projective tensor products. We notice that $(A(G),\ast)$ is an operator algebra and observe an unexpected set of spectral synthesis.
Development of Composite Wicks for Heat Pipe Performance Enhancement

This study examines the enhancement of heat pipe thermal performance through the employment of composite wicks. Wicks were fabricated from a biporous structure comprised of fine nickel metal powders sintered onto layers of coarse pore copper mesh. Wick structures were designed to explore the effects of both enhanced evaporation heat transfer at the liquid/vapor interface and the extension of the capillary limit. A number of composite wick heat pipe configurations were fabricated and tested to assess performance improvements in comparison to conventional designs. Horizontal, gravity-assisted, and against-gravity tests were conducted to determine whether these designs were orientation-dependent. At various heat inputs, some configurations achieved thermal performance levels greater than three times higher than those of conventional heat pipes. During against-gravity tests, virtually all composite designs exhibited improved performance over the conventional heat pipe at all heat inputs. These results clearly demonstrated that significant improvements in heat pipe performance were achieved through composite wick design.
Resonant excitonic emission of a single quantum dot in the Rabi regime

We report on coherent resonant emission of the fundamental exciton state in a single semiconductor GaAs quantum dot. A resonant regime with picosecond laser excitation is realized by embedding the quantum dots in a one-dimensional waveguiding structure. As the pulse intensity is increased, Rabi oscillation is observed up to three periods. The Rabi regime is achieved owing to an enhanced light-matter coupling in the waveguide but with different dynamics with respect to usual cavity quantum electrodynamics. The resonant control of the quantum dot fundamental transition opens new possibilities in quantum state manipulation and quantum optics experiments in condensed-matter physics.
Diophantine approximation exponents on homogeneous varieties

Recent years have seen very important developments at the interface of Diophantine approximation and homogeneous dynamics. In the first part of the paper we give a brief exposition of a dictionary developed by Dani and Kleinbock-Margulis which relates Diophantine properties of vectors to distribution of orbits of flows on the space of unimodular lattices. In the second part of the paper we briefly describe an extension of this dictionary recently developed by the authors, which establishes an analogous dynamical correspondence for general lattice orbits on homogeneous spaces. We concentrate specifically on the problem of estimating exponents of Diophantine approximation by arithmetic lattices acting on algebraic varieties. In the third part of the paper, we exemplify our results by establishing explicit bounds for the Diophantine exponent of dense lattice orbits in a number of basic cases. These include the linear and affine actions on affine spaces, and the action on the variety of matrices of fixed determinant. In some cases, these exponents are shown to be best possible.
Harnessing symmetry to control quantum transport

Controlling transport in quantum systems holds the key to many promising quantum technologies. Here we review the power of symmetry as a resource to manipulate quantum transport and apply these ideas to engineer novel quantum devices. Using tools from open quantum systems and large deviation theory, we show that symmetry-mediated control of transport is enabled by a pair of twin dynamic phase transitions in current statistics, accompanied by a coexistence of different transport channels. By playing with the symmetry decomposition of the initial state, one can modulate the importance of the different transport channels and hence control the flowing current. Motivated by the problem of energy harvesting, we illustrate these ideas in open quantum networks, an analysis that leads to the design of a symmetry-controlled quantum thermal switch. We review an experimental setup recently proposed for symmetry-mediated quantum control in the lab based on a linear array of atom-doped optical cavities, and the possibility of using transport as a probe to uncover hidden symmetries, as recently demonstrated in molecular junctions, is also discussed. Other symmetry-mediated control mechanisms are also described. Overall, these results demonstrate the importance of symmetry not only as an organizing principle in physics but also as a tool to control quantum systems.
Everywhere divergence of the one-sided ergodic Hilbert transform and Liouville numbers

We prove some results on the behavior of infinite sums of the form $\Sigma f\circ T^n(x)\frac{1}{n}$, where $T:S^1\to S^1$ is an irrational circle rotation and $f$ is a mean-zero function on $S^1$. In particular, we show that for a certain class of functions $f$, there are Liouville $\alpha$ for which this sum diverges everywhere. We also show that there are Liouville $\alpha$ for which the sum converges everywhere.
On the initial value problem for the Navier-Stokes equations with the initial datum in the Sobolev spaces

In this paper, we study local well-posedness for the Navier-Stokes equations with arbitrary initial data in homogeneous Sobolev spaces $\dot{H}^s_p(\mathbb{R}^d)$ for $d \geq 2, p > \frac{d}{2},\ {\rm and}\ \frac{d}{p} - 1 \leq s d$ and $s = 0$ (see M. Cannone (1995), M. Cannone and Y. Meyer (1995)). In the case of critical indexes $s=\frac{d}{p}-1$, we prove global well-posedness for Navier-Stokes equations when the norm of the initial value is small enough. This result is a generalization of the ones in Cannone (1999) and P. G. Lemarie-Rieusset (2002) in which $(p = d, s = 0)$ and $(p > d, s = \frac{d}{p} - 1)$, respectively.
Measuring the Baryon Acoustic Oscillation scale using the Sloan Digital Sky Survey and 2dF Galaxy Redshift Survey

We introduce a method to constrain general cosmological models using Baryon Acoustic Oscillation (BAO) distance measurements from galaxy samples covering different redshift ranges, and apply this method to analyse samples drawn from the Sloan Digital Sky Survey (SDSS) and 2dF Galaxy Redshift Survey (2dFGRS). BAOs are detected in the clustering of the combined 2dFGRS and SDSS main galaxy samples, and measure the distance–redshift relation at z= 0.2. BAOs in the clustering of the SDSS luminous red galaxies measure the distance–redshift relation at z= 0.35. The observed scales of the BAOs calculated from these samples and from the combined sample are jointly analysed using estimates of the correlated errors, to constrain the form of the distance measure DV(z) ≡[(1 +z)2D2Acz/H(z)]1/3. Here DA is the angular diameter distance, and H(z) is the Hubble parameter. This gives rs/DV(0.2) = 0.1980 ± 0.0058 and rs/DV(0.35) = 0.1094 ± 0.0033 (1σ errors), with a correlation coefficient of 0.39, where rs is the comoving sound horizon scale at recombination. Matching the BAOs to have the same measured scale at all redshifts then gives DV(0.35)/DV(0.2) = 1.812 ± 0.060. The recovered ratio is roughly consistent with that predicted by the higher redshift Supernova Legacy Survey (SNLS) supernova data for Λ cold dark matter cosmologies, but does require slightly stronger cosmological acceleration at a low redshift. If we force the cosmological model to be flat with constant w, then we find Ωm= 0.249 ± 0.018 and w=−1.004 ± 0.089 after combining with the SNLS data, and including the WMAP measurement of the apparent acoustic horizon angle in the cosmic microwave background.
Dynamics on asymptotically conical geometries

We obtain general results on the dynamics of exactly conical geometries, where we use the notion of boundaries at infinity to characterize asymptotic behavior. As we demonstrate in examples, these notions also apply to smooth geometries that are merely asymptotically conical, such as the Eguchi-Hanson or resolved conifold geometries. In these cases we obtain a rather complete qualitative understanding of the varieties of asymptotic behavior, and we probe the connectivity of the phase space by finding infinitely large families of multiple geodesics connecting a point on the infinite past boundary with a point in the infinite future boundary.
On sublinear bilipschitz equivalence of groups

We discuss the notion of sublinearly bilipschitz equivalences (SBE), which generalize quasi-isometries, allowing some additional terms that behave sublinearly with respect to the distance from the origin. Such maps were originally motivated by the fact they induce bilipschitz homeomorphisms between asymptotic cones. We prove here that for hyperbolic groups, they also induce Holder homeomorphisms between the boundaries. This yields many basic examples of hyperbolic groups that are pairwise non-SBE. Besides, we check that subexponential growth is an SBE-invariant. The central part of the paper addresses nilpotent groups. While classification up to sublinearly bilipschitz equivalence is known in this case as a consequence of Pansu's theorems, its quantitative version is not. We introduce a computable algebraic invariant $e=e_G<1$ for every such group $G$, and check that $G$ is $O(r^e)$-bilipschitz equivalent to its associated Carnot group. Here $r\mapsto r^e$ is a quantitive sublinear bound. Finally, we define the notion of large-scale contractable and large-scale homothetic metric spaces. We check that these notions imply polynomial growth under general hypotheses, and formulate conjectures about groups with these properties.
X-Ray Timing of PSR J1852+0040 in Kesteven 79: Evidence of Neutron Stars Weakly Magnetized at Birth

The 105 ms X-ray pulsar J1852+0040 is the central compact object (CCO) in supernova remnant Kes 79. We report a sensitive upper limit on its radio flux density of 12 μJy at 2 GHz using the NRAO Green Bank Telescope. Timing using the Newton X-Ray Multi-Mirror Mission (XMM-Newton) and the Chandra X-Ray Observatory over a 2.4 yr span reveals no significant change in its spin period. The 2 σ upper limit on the period derivative leads, in the dipole spin-down formalism, to an energy loss rate Ė < 7 × 1033 ergs s-1, surface magnetic field strength Bp < 1.5 × 1011 G, and characteristic age τc ≡ P/2 Ṗ > 8 Myr. This value of τc exceeds the age of the SNR by 3 orders of magnitude, implying that the pulsar was born spinning at its current period. However, the X-ray luminosity of Lbol ≈ 3 × 1033(d/7.1 kpc)2 ergs s-1 is a large fraction of Ė, which challenges the rotation-powered assumption. Instead, its high blackbody temperature kTBB = 0.46 ± 0.04 keV, small blackbody radius RBB ≈ 0.8 km, and large pulsed fraction fp ≈ 80% may be evidence of accretion onto a polar cap, possibly from a fallback disk made of supernova debris. If Bp < 1010 G, an accretion disk can penetrate the light cylinder and interact with the magnetosphere, while resulting torques on the neutron star remain within the observed limits. A weak B field is also inferred in another CCO, the 424 ms pulsar, from its steady spin and soft X-ray absorption lines. We propose this origin of radio-quiet CCOs: the magnetic field, derived from a turbulent dynamo, is weaker if the neutron star is formed spinning slowly, which enables it to accrete supernova debris. Accretion excludes neutron stars born with both Bp < 1011 G and P > 0.1 s from radio pulsar surveys, where Bp < 1011 G is not encountered except among very old (τc > 40 Myr) or recycled pulsars. Finally, such a CCO, if born in SN 1987A, could explain the nondetection of a pulsar there.
Augmented Lagrangian-Based Decomposition Methods with Non-Ergodic Optimal Rates

We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel combination of the augmented Lagrangian framework, partial alternating/linearization scheme, Nesterov's acceleration technique, and adaptive strategy. The proposed algorithms have the following new features compared to existing ADMM variants. First, they have a Nesterov's acceleration step on the primal variables instead of the dual ones as in several ADMM variants. Second, they possess an optimal $O(\frac{1}{k})$-convergence rate guarantee in a non-ergodic sense without any smoothness or strong convexity-type assumption, where $k$ is the iteration counter. When one objective term is strongly convex, our algorithm achieves an optimal $O(\frac{1}{k^2})$-non-ergodic rate. Third, our methods have better per-iteration complexity than standard ADMM due to the linearization step in the second subproblem. Fourth, we provide a set of conditions to derive update rules for algorithmic parameters, and give a concrete update for these parameters as an example. Finally, when the objective function is separable, our methods can naturally be implemented in a parallel fashion. We also study two extensions of our methods and a connection to existing primal-dual methods. We verify our theoretical development via different numerical examples and compare our methods with some existing state-of-the-art algorithms.
Topological stability and pseudo-orbit tracing property of group actions

In this note we extend the concept of topological stability from homeomorphisms to group actions on compact metric spaces, and prove that if an action of a finitely generated group is expansive and has the pseudo-orbit tracing property then it is topologically stable. This represents a group action version of the Walter's stability theorem. Moreover we give a class of group actions with topological stability or pseudo-orbit tracing property. On the other hand, we also provide a characterization of subshifts of finite type over finitely generated groups in term of pseudo-orbit tracing property.
Approximate symmetries of Hamiltonians

We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by showing that approximate symmetry operators---unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small---which possess certain mutual commutation relations can be restricted to the ground space with low distortion. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations, and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space, and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators which may be of independent interest.
Standard Errors of Correlations Adjusted for Incidental Selection

The standard error of correlations that have been adjusted for selection with commonly used formulas developed by Pearson (1903) was investigated. The major purposes of the study were (1) to provide large- sample approximations of the standard error of a cor relation adjusted using the Pearson-Lawley three-varia ble correction formula; (2) to examine the standard er rors of adjusted correlations under specific conditions; and (3) to compare various estimates of the standard errors under direct and indirect selection. Two theory- based large-sample estimates of the standard error of a correlation adjusted for indirect selection were devel oped using the delta method. These two estimates were compared to one another, to a bootstrap esti mate, and to an empirical standard deviation of a se ries of adjusted correlations generated in a simulation study. The simulation study manipulated factors de fined by sample size, selection ratio, underlying popu lation distribution, and population correlations in situ ations that satisfied the basic assumptions of the Pearson-Lawley procedures. The results indicated that the large-sample and bootstrap estimates were very similar when the sample size was 500 and, in most cases, the simpler of the two large-sample approxima tions appears to offer a reasonable estimate of the standard error of an adjusted correlation without re sorting to complex, computer-intensive approaches. Index terms: correlation coefficients, missing data, Pearson-Lawley corrections, selection, standard er rors of correlations, validity studies.
Knot traces and concordance

We give a method for constructing many pairs of distinct knots K0 and K1 such that the two 4‐manifolds obtained by attaching a 2‐handle to B4 along Ki with framing zero are diffeomorphic. We use the d‐invariants of Heegaard Floer homology to obstruct the smooth concordance of some of these K0 and K1 , thereby disproving a conjecture of Abe. As a consequence, we obtain a proof that there exist patterns P in solid tori such that P(K) is not always concordant to P(U)#K and yet whose action on the smooth concordance group is invertible.
Endgames in bidding chess

Bidding chess is a chess variant where instead of alternating play, players bid for the opportunity to move. Generalizing a known result on so-called Richman games, we show that for a natural class of games including bidding chess, each position can be assigned rational upper and lower values corresponding to the limit proportion of money that Black (say) needs in order to force a win and to avoid losing, respectively. We have computed these values for all three-piece endgames, and in all cases, the upper and lower values coincide. Already with three pieces, the game is quite complex, and the values have denominators of up to 138 digits.