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MIT Open Access Articles

Mostrando recursos 1 - 20 de 13,379

1.
On the Spectrum of Lattice Massive SU(2) Yang–Mills - Ferrari, Ruggero
On the basis of extended simulations, we provide some results concerning the spectrum of Massive SU(2) Yang–Mills on the lattice. We study the “time” correlator of local gauge invariant operators integrated over the remaining three dimensions. The energy gaps are measured in the isospin I = 0,1 and internal spin J = 0,1 channels. No correlation is found in the I = 1, J = 0 channel. In the I = 1, J = 1 channel and far from the critical mass value m[subscript c], the energy gap roughly follows the bare value m (vector mesons). In approaching the critical...

2.
The SU(2) ⊗ U(1) Electroweak Model Based on the Nonlinearly Realized Gauge Group. II. Functional Equations and the Weak Power-Counting - Bettinelli, D.; Ferrari, Ruggero; Quadri, A.
In the present paper, that is the second part devoted to the construction of an electroweak model based on a nonlinear realization of the gauge group SU(2) ⊗ U(1), we study the tree-level vertex functional with all the sources necessary for the functional formulation of the relevant symmetries (Local Functional Equation, Slavnov–Taylor identity, Landau Gauge Equation) and for the symmetric removal of the divergences. The Weak Power Counting criterion is proven in the presence of the novel sources. The local invariant solutions of the functional equations are constructed in order to represent the counterterms for the one-loop subtractions. The bleaching...

3.
ebalance: A Stata Package for Entropy Balancing - Hainmueller, Jens; Su, Yiqing; Xu, Yiqing
The Stata package ebalance implements entropy balancing, a multivariate reweighting method described in Hainmueller (2012 ) that allows users to reweight a dataset such that the covariate distributions in the reweighted data satisfy a set of specified moment conditions. This can be useful to create balanced samples in observational studies with a binary treatment where the control group data can be reweighted to match the covariate moments in the treatment group. Entropy balancing can also be used to reweight a survey sample to known characteristics from a target population.

4.
Hypoxia shifts activity of neuropeptide Y in Ewing sarcoma from growth-inhibitory to growth-promoting effects - Lu, Congyi
Ewing sarcoma (ES) is an aggressive malignancy driven by an oncogenic fusion protein, EWS-FLI1. Neuropeptide Y (NPY), and two of its receptors, Y1R and Y5R are up-regulated by EWS-FLI1 and abundantly expressed in ES cells. Paradoxically, NPY acting via Y1R and Y5R stimulates ES cell death. Here, we demonstrate that these growth-inhibitory actions of NPY are counteracted by hypoxia, which converts the peptide to a growth-promoting factor. In ES cells, hypoxia induces another NPY receptor, Y2R, and increases expression of dipeptidyl peptidase IV (DPPIV), an enzyme that cleaves NPY to a shorter form, NPY3-36. This truncated peptide no longer binds...

5.
New Spectral Bounds on the Chromatic Number Encompassing all Eigenvalues of the Adjacency Matrix - Wocjan, Pawel; Elphick, Clive
The purpose of this article is to improve existing lower bounds on the chromatic number χ. Let μ[subscript 1],…,μ[subscript n] be the eigenvalues of the adjacency matrix sorted in non-increasing order.
First, we prove the lower bound χ ≥ 1 + max[subscript m]{∑[m over i=1]μ[subscript i]/ − ∑[m over i=1]μ[subscript n−i+1]} for m = 1,…,n − 1. This generalizes the Hoffman lower bound which only involves the maximum and minimum eigenvalues, i.e., the case m = 1. We provide several examples for which the new bound exceeds the Hoffman lower bound.
Second, we conjecture the lower bound χ ≥ 1 + s[superscript...

6.
Two Remarks on Skew Tableaux - Stanley, Richard P.
This paper contains two results on the number f[superscript σ/τ] of standard skew Young tableaux of shape σ/τ. The first concerns generating functions for certain classes of "periodic" shapes related to work of Gessel-Viennot and Baryshnikov-Romik. The second result gives an evaluation of the skew Schur function s[subscript λ/μ](x) at x = (1,1/2[superscript 2k],1/3[superscript 2k],…) for k = 1,2,3 in terms of f[superscript σ/τ] for a certain skew shape σ/τ depending on λ/μ.

7.
Hurwitz Equivalence in Tuples of Dihedral Groups, Dicyclic Groups, and Semidihedral Groups - Sia, Charmaine
Let D[subscript 2N] be the dihedral group of order 2N, Dic[subscript 4M] the dicyclic group of order 4M, SD[subscript 2m] the semidihedral group of order 2[superscript m], and M[subscript 2m] the group of order 2[superscript m] with presentation
M[subscript 2m] = ⟨α,β∣α[superscript 2m−1] = β[superscript 2] = 1, βαβ[superscript −1] = α[superscript 2m−2+1]⟩.
We classify the orbits in D[n over 2N], Dic[n over 4M], SD[n over 2m], and M[n over 2m] under the Hurwitz action.

8.
Demazure Crystals, Kirillov-Reshetikhin Crystals, and the Energy Function - Schilling, Anne; Tingley, Peter
It has previously been shown that, at least for non-exceptional Kac-Moody Lie algebras, there is a close connection between Demazure crystals and tensor products of Kirillov-Reshetikhin crystals. In particular, certain Demazure crystals are isomorphic as classical crystals to tensor products of Kirillov-Reshetikhin crystals via a canonically chosen isomorphism. Here we show that this isomorphism intertwines the natural affine grading on Demazure crystals with a combinatorially defined energy function. As a consequence, we obtain a formula of the Demazure character in terms of the energy function, which has applications to Macdonald polynomials and q-deformed Whittaker functions.

9.
A Finite Calculus Approach to Ehrhart Polynomials - Sam, Steven V.; Woods, Kevin M.
A rational polytope is the convex hull of a finite set of points in R[superscript d] with rational coordinates. Given a rational polytope P⊆R[superscript d], Ehrhart proved that, for t∈Z≥[subscript 0[, the function #(tP∩Z[superscript d]) agrees with a quasi-polynomial L[subscript P](t), called the Ehrhart quasi-polynomial. The Ehrhart quasi-polynomial can be regarded as a discrete version of the volume of a polytope. We use that analogy to derive a new proof of Ehrhart's theorem. This proof also allows us to quickly prove two other facts about Ehrhart quasi-polynomials: McMullen's theorem about the periodicity of the individual coefficients of the quasi-polynomial and...

10.
Pattern Popularity in 132-Avoiding Permutations - Rudolph, Kate
The popularity of a pattern p is the total number of copies of p within all permutations of a set. We address popularity in the set of 132-avoidng permutations. Bona showed that in this set, all other non-monotone length-3 patterns are equipopular, and proved equipopularity relations between some length-k patterns of a specific form. We prove equipopularity relations between general length-k patterns, based on the structure of their corresponding binary plane trees. Our result explains all equipopularity relations for patterns of length up to 7, and we conjecture that it provides a complete classification of equipopularity in 132-avoiding permutations.

11.
Detecting topological currents in graphene superlattices - Gorbachev, R. V.; Yu, G. L.; Kretinin, A. V.; Withers, F.; Cao, Y.; Mishchenko, A.; Grigorieva, I. V.; Novoselov, K. S.; Geim, A. K.; Song, Justin Chien Wen; Levitov, Leonid
Topological materials may exhibit Hall-like currents flowing transversely to the applied electric field even in the absence of a magnetic field. In graphene superlattices, which have broken inversion symmetry, topological currents originating from graphene's two valleys are predicted to flow in opposite directions and combine to produce long-range charge neutral flow. We observe this effect as a nonlocal voltage at zero magnetic field in a narrow energy range near Dirac points at distances as large as several microns away from the nominal current path. Locally, topological currents are comparable in strength to the applied current, indicating large valley-Hall angles. The...

12.
Trees with an On-Line Degree Ramsey Number of Four - Rolnick, David S.
On-line Ramsey theory studies a graph-building game between two players. The player called Builder builds edges one at a time, and the player called Painter paints each new edge red or blue after it is built. The graph constructed is called the background graph. Builder's goal is to cause the background graph to contain a monochromatic copy of a given goal graph, and Painter's goal is to prevent this. In the S[subscript k]-game variant of the typical game, the background graph is constrained to have maximum degree no greater than k. The on-line degree Ramsey number [˚over R][subscript Δ](G) of...

13.
Sortable Elements for Quivers with Cycles - Reading, Nathan; Speyer, David E.
Each Coxeter element c of a Coxeter group W defines a subset of W called the c-sortable elements. The choice of a Coxeter element of W is equivalent to the choice of an acyclic orientation of the Coxeter diagram of W. In this paper, we define a more general notion of Ω-sortable elements, where Ω is an arbitrary orientation of the diagram, and show that the key properties of c-sortable elements carry over to the Ω-sortable elements. The proofs of these properties rely on reduction to the acyclic case, but the reductions are nontrivial; in particular, the proofs rely on...

14.
A Case for Leveraging 802.11p for Direct Phone-to-Phone Communications - Choi, Pilsoon; Gao, Jason Hao; Ramanathan, Nadesh; Mao, Mengda; Xu, Shipeng; Boon, Chirn-Chye; Fahmy, Suhaib A.; Peh, Li-Shiuan
WiFi cannot effectively handle the demands of device-to-device communication between phones, due to insufficient range and poor reliability. We make the case for using IEEE 802.11p DSRC instead, which has been adopted for vehicle-to-vehicle communications, providing lower latency and longer range. We demonstrate a prototype motivated by a novel fabrication process that deposits both III-V and CMOS devices on the same die. In our system prototype, the designed RF front-end is interfaced with a baseband processor on an FPGA, connected to Android phones. It consumes 0.02uJ/bit across 100m assuming free space. Application-level power control dramatically reduces power consumption by 47-56%.

15.
RoadRunner: Infrastructure-less vehicular congestion control - Gao, Jason Hao; Peh, Li-Shiuan
RoadRunner is an in-vehicle app for traffic congestion control without costly roadside infrastructure, instead judiciously harnessing vehicle-to-vehicle communications, cellular connectivity, and onboard computation and sensing to enable large-scale traffic congestion control at higher penetration and finer granularity than previously possible. RoadRunner limits the number of vehicles in a congested region or road by requiring each to possess a token for entry. Tokens can circulate and be reused among multiple vehicles as vehicles move between regions. We built RoadRunner as an Android app utilizing LTE, 802.11p, and 802.11n radios, deployed it on 10 vehicles, and measured cellular access reductions of up...

16.
Reconstructing Permutations from Cycle Minors - Monks, Maria
The ith cycle minor of a permutation p of the set {1,2,…,n} is the permutation formed by deleting an entry i from the decomposition of p into disjoint cycles and reducing each remaining entry larger than i by 1. In this paper, we show that any permutation of {1,2,…,n} can be reconstructed from its set of cycle minors if and only if n≥6. We then use this to provide an alternate proof of a known result on a related reconstruction problem.

17.
Schur Times Schubert via the Fomin-Kirillov Algebra - Meszaros, Karola; Panova, Greta; Postnikov, Alexander
We study multiplication of any Schubert polynomial S[subscript w] by a Schur polynomial sλ (the Schubert polynomial of a Grassmannian permutation) and the expansion of this product in the ring of Schubert polynomials. We derive explicit nonnegative combinatorial expressions for the expansion coefficients for certain special partitions λ, including hooks and the 2×2 box. We also prove combinatorially the existence of such nonnegative expansion when the Young diagram of λ is a hook plus a box at the (2,2) corner. We achieve this by evaluating Schubert polynomials at the Dunkl elements of the Fomin-Kirillov algebra and proving special cases of...

18.
Actions and Identities on Set Partitions - Marberg, Eric
A labeled set partition is a partition of a set of integers whose arcs are labeled by nonzero elements of an abelian group A. Inspired by the action of the linear characters of the unitriangular group on its supercharacters, we define a group action of A[superscript n] on the set of A-labeled partitions of an (n+1)-set. By investigating the orbit decomposition of various families of set partitions under this action, we derive new combinatorial proofs of Coker's identity for the Narayana polynomial and its type B analogue, and establish a number of other related identities. In return, we also prove...

19.
Pilot-wave hydrodynamics - Bush, John W. M.
Yves Couder, Emmanuel Fort, and coworkers recently discovered that a millimetric droplet sustained on the surface of a vibrating fluid bath may self-propel through a resonant interaction with its own wave field. This article reviews experimental evidence indicating that the walking droplets exhibit certain features previously thought to be exclusive to the microscopic, quantum realm. It then reviews theoretical descriptions of this hydrodynamic pilot-wave system that yield insight into the origins of its quantumlike behavior. Quantization arises from the dynamic constraint imposed on the droplet by its pilot-wave field, and multimodal statistics appear to be a feature of chaotic pilot-wave...

20.
Generating Trees and Pattern Avoidance in Alternating Permutations - Lewis, Joel Brewster
We extend earlier work of the same author to enumerate alternating permutations avoiding the permutation pattern 2143. We use a generating tree approach to construct a recursive bijection between the set A[subscript 2n](2143) of alternating permutations of length 2n avoiding 2143 and the set of standard Young tableaux of shape ⟨n,n,n⟩, and between the set A[subscript 2n+1](2143) of alternating permutations of length 2n+1 avoiding 2143 and the set of shifted standard Young tableaux of shape ⟨n+2,n+1,n⟩. We also give a number of conjectures and open questions on pattern avoidance in alternating permutations and generalizations thereof.