A local-global principle for linear dependence of noncommutative polynomials

A set of polynomials in noncommuting variables is called locally linearly dependent if their evaluations at tuples of matrices are always linearly dependent. By a theorem of Camino, Helton, Skelton and Ye, a finite locally linearly dependent set of polynomials is linearly dependent. In this short note an alternative proof based on the theory of polynomial identities is given. The method of the proof yields generalizations to directional local linear dependence and evaluations in general algebras over fields of arbitrary characteristic. A main feature of the proof is that it makes it possible to deduce bounds on the size of the matrices where the (directional) local linear dependence needs to be tested in order to establish linear dependence.Comment: 8 page

On the class SI of J-contractive functions intertwining solutions of linear differential equations

In the PhD thesis of the second author under the supervision of the third author was defined the class SI of J-contractive functions, depending on a parameter and arising as transfer functions of overdetermined conservative 2D systems invariant in one direction. In this paper we extend and solve in the class SI, a number of problems originally set for the class SC of functions contractive in the open right-half plane, and unitary on the imaginary line with respect to some preassigned signature matrix J. The problems we consider include the Schur algorithm, the partial realization problem and the Nevanlinna-Pick interpolation problem. The arguments rely on a correspondence between elements in a given subclass of SI and elements in SC. Another important tool in the arguments is a new result pertaining to the classical tangential Schur algorithm.Comment: 46 page

Quantum Criticality

This is a review of the basic theoretical ideas of quantum criticality, and of their connection to numerous experiments on correlated electron compounds. A shortened, modified, and edited version appeared in Physics Today. This arxiv version has additional citations to the literature.Comment: 17 pages, 7 figures; (v2) added ref

PML::RARA and GATA2 proteins interact via DNA templates to induce aberrant self-renewal in mouse and human hematopoietic cells

The underlying mechanism(s) by which the PML::RARA fusion protein initiates acute promyelocytic leukemia is not yet clear. We defined the genomic binding sites of PML::RARA in primary mouse and human hematopoietic progenitor cells with V5-tagged PML::RARA, using anti-V5-PML::RARA chromatin immunoprecipitation sequencing and CUT&RUN approaches. Most genomic PML::RARA binding sites were found in regions that were already chromatin-accessible (defined by ATAC-seq) in unmanipulated, wild-type promyelocytes, suggesting that these regions are open prior to PML::RARA expression. We found that GATA binding motifs, and the direct binding of the chromatin pioneering factor GATA2, were significantly enriched near PML::RARA binding sites. Proximity labeling studies revealed that PML::RARA interacts with ~250 proteins in primary mouse hematopoietic cells; GATA2 and 33 others require PML::RARA binding to DNA for the interaction to occur, suggesting that binding to their cognate DNA target motifs may stabilize their interactions. In the absence o

Universal Signatures of Fractionalized Quantum Critical Points

Groundstates of certain materials can support exotic excitations with a charge that's a fraction of the fundamental electron charge. The condensation of these fractionalized particles has been predicted to drive novel quantum phase transitions, which haven't yet been observed in realistic systems. Through numerical and theoretical analysis of a physical model of interacting lattice bosons, we establish the existence of such an exotic critical point, called XY*. We measure a highly non-classical critical exponent eta = 1.49(2), and construct a universal scaling function of winding number distributions that directly demonstrates the distinct topological sectors of an emergent Z_2 gauge field. The universal quantities used to establish this exotic transition can be used to detect other fractionalized quantum critical points in future model and material systems.Comment: 12 pages, 3 figures (+ supplemental

Go-stimuli proportion influences response strategy in a sustained attention to response task

The sustained attention to response task (SART) usefulness as a measure of sustained attention has been questioned. The SART may instead be a better measure of other psychological processes and could prove useful in understanding some real-world behaviours. Thirty participants completed four Go/No-Go response tasks much like the SART, with Go-stimuli proportions of .50, .65, .80 and .95. As Go-stimuli proportion increased, reaction times decreased while both commission errors and self-reported task-related thoughts increased. Performance measures were associated with task-related thoughts but not taskunrelated thoughts. Instead of faster reaction times and increased commission errors being due to absentmindedness or perceptual decoupling from the task, the results suggested participants made use of two competing response strategies, in line with a response strategy or response inhibition perspective of SART performance. Interestingly, performance measures changed in a nonlinear manner, despite the linear Go proportion increase. A threshold may exist where the prepotent motor response becomes more pronounced, leading to the disproportionate increase in response speed and commission errors. This research has implications for researchers looking to employ the SAR

Can Quantum de Sitter Space Have Finite Entropy?

If one tries to view de Sitter as a true (as opposed to a meta-stable) vacuum, there is a tension between the finiteness of its entropy and the infinite-dimensionality of its Hilbert space. We invetsigate the viability of one proposal to reconcile this tension using $q$-deformation. After defining a differential geometry on the quantum de Sitter space, we try to constrain the value of the deformation parameter by imposing the condition that in the undeformed limit, we want the real form of the (inherently complex) quantum group to reduce to the usual SO(4,1) of de Sitter. We find that this forces $q$ to be a real number. Since it is known that quantum groups have finite-dimensional representations only for $q=$ root of unity, this suggests that standard $q$-deformations cannot give rise to finite dimensional Hilbert spaces, ruling out finite entropy for q-deformed de Sitter.Comment: 10 pages, v2: references added, v3: minor corrections, abstract and title made more in-line with the result, v4: published versio