Separable Subsets Research Articles

Characterization of enhancer fragments in Drosophila robo2

ABSTRACT Receptor proteins of the Roundabout (Robo) family regulate axon guidance decisions during nervous system development. Among the three Drosophila robo family genes (robo1, robo2 and robo3), robo2 displays a dynamic expression pattern and regulates multiple axon guidance outcomes, including preventing midline crossing in some axons, promoting midline crossing in others, forming lateral longitudinal axon pathways, and regulating motor axon guidance. The identity and location of enhancer elements regulating robo2’s complex and dynamic expression pattern in different neural cell types are unknown. Here, we characterize a set of 17 transgenic lines expressing GAL4 under the control of DNA sequences derived from noncoding regions in and around robo2, to identify enhancers controlling specific aspects of robo2 expression in the embryonic ventral nerve cord. We identify individual fragments that confer expression in specific cell types where robo2 is known to function, including early pioneer neurons, midline glia and lateral longitudinal neurons. Our results indicate that robo2’s dynamic expression pattern is specified by a combination of enhancer elements that are active in different subsets of cells. We show that robo2’s expression in lateral longitudinal axons represents two genetically separable subsets of neurons, and compare their axon projections with each other and with Fasciclin II (FasII), a commonly used marker of longitudinal axon pathways. In addition, we provide a general description of each fragment’s expression in embryonic tissues outside of the nervous system, to serve as a resource for other researchers interested in robo2 expression and its functional roles outside the central nervous system.

Hybrid quantum-classical reservoir computing of thermal convection flow

We simulate the nonlinear chaotic dynamics of Lorenz-type models for a classical two-dimensional thermal convection flow with three and eight degrees of freedom by a hybrid quantum-classical reservoir computing model. The high-dimensional quantum reservoir dynamics are established by universal quantum gates that rotate and entangle the individual qubits of the tensor product quantum state. A comparison of the quantum reservoir computing model with its classical counterpart shows that the same prediction and reconstruction capabilities of classical reservoirs with thousands of perceptrons can be obtained by a few strongly entangled qubits. We demonstrate that the mean squared error between model output and ground truth in the test phase of the quantum reservoir computing algorithm increases when the reservoir is decomposed into separable subsets of qubits. Furthermore, the quantum reservoir computing model is implemented on a real noisy IBM quantum computer for up to seven qubits. Our work thus opens the door to model the dynamics of classical complex systems in a high-dimensional phase space effectively with an algorithm that requires a small number of qubits.

Type I Interferons Promote Germinal Centers Through B Cell Intrinsic Signaling and Dendritic Cell Dependent Th1 and Tfh Cell Lineages.

Type I interferons (IFNs) are essential for antiviral immunity, appear to represent a key component of mRNA vaccine-adjuvanticity, and correlate with severity of systemic autoimmune disease. Relevant to all, type I IFNs can enhance germinal center (GC) B cell responses but underlying signaling pathways are incompletely understood. Here, we demonstrate that a succinct type I IFN response promotes GC formation and associated IgG subclass distribution primarily through signaling in cDCs and B cells. Type I IFN signaling in cDCs, distinct from cDC1, stimulates development of separable Tfh and Th1 cell subsets. However, Th cell-derived IFN-γ induces T-bet expression and IgG2c isotype switching in B cells prior to this bifurcation and has no evident effects once GCs and bona fide Tfh cells developed. This pathway acts in synergy with early B cell-intrinsic type I IFN signaling, which reinforces T-bet expression in B cells and leads to a selective amplification of the IgG2c+ GC B cell response. Despite the strong Th1 polarizing effect of type I IFNs, the Tfh cell subset develops into IL-4 producing cells that control the overall magnitude of the GCs and promote generation of IgG1+ GC B cells. Thus, type I IFNs act on B cells and cDCs to drive GC formation and to coordinate IgG subclass distribution through divergent Th1 and Tfh cell-dependent pathways.

The Voter Basis and the Admissibility of Tree Characters

Let ≽ be a total order on the power set of a finite set [n]. A subset S ⊂ [n] is separable when for any X,Y ⊂ S and any Z ⊂ [n] − S, the ordering of X and Y is the same as the ordering of X ∪ Z and Y ∪ Z. The character of a preference order is the collection of all separable subsets. Motivated by questions in the theories of voting, marketing and social choice, the admissibility problem asks which collections \(\mathcal {C} \subset \mathcal {P}({[n]})\) can arise as characters of preference orders. We introduce a linear algebraic technique to construct preference orders. Each vector in our 2n-dimensional voter basis induces a simple preference preorder (where ties are allowed) with nice separability properties. Given any collection \(\mathcal {C} \subset \mathcal {P}({[n]})\) that contains both ∅ and [n], and such that all pairs of subsets are either nested or disjoint, we use the voter basis to construct a preference order with character \(\mathcal {C}\).

Dissociable control of unconditioned responses and associative fear learning by parabrachial CGRP neurons

Parabrachial CGRP neurons receive diverse threat-related signals and contribute to multiple phases of adaptive threat responses in mice, with their inactivation attenuating both unconditioned behavioral responses to somatic pain and fear-memory formation. Because CGRPPBN neurons respond broadly to multi-modal threats, it remains unknown how these distinct adaptive processes are individually engaged. We show that while three partially separable subsets of CGRPPBN neurons broadly collateralize to their respective downstream partners, individual projections accomplish distinct functions: hypothalamic and extended amygdalar projections elicit assorted unconditioned threat responses including autonomic arousal, anxiety, and freezing behavior, while thalamic and basal forebrain projections generate freezing behavior and, unexpectedly, contribute to associative fear learning. Moreover, the unconditioned responses generated by individual projections are complementary, with simultaneous activation of multiple sites driving profound freezing behavior and bradycardia that are not elicited by any individual projection. This semi-parallel, scalable connectivity schema likely contributes to flexible control of threat responses in unpredictable environments.

Distinct Mechanisms of Over-Representation of Landmarks and Rewards in the Hippocampus

In the hippocampus, locations associated with salient features are represented by a disproportionately large number of neurons, but the cellular and molecular mechanisms underlying this over-representation remain elusive. Using longitudinal calcium imaging in mice learning to navigate in virtual reality, we find that the over-representation of reward and landmark locations are mediated by persistent and separable subsets of neurons, with distinct time courses of emergence and differing underlying molecular mechanisms. Strikingly, we find that in mice lacking Shank2, an autism spectrum disorder (ASD)-linked gene encoding an excitatory postsynaptic scaffold protein, the learning-induced over-representation of landmarks was absent whereas the over-representation of rewards was substantially increased, as was goal-directed behavior. These findings demonstrate that multiple hippocampal coding processes for unique types of salient features are distinguished by a Shank2-dependent mechanism and suggest that abnormally distorted hippocampal salience mapping may underlie cognitive and behavioral abnormalities in a subset of ASDs.

Leveraging design diversity to counteract process variation: theory, method, and FPGAtoolchain to increase yield and resiliencein‐situ

With continued scaling of integrated circuits into deep nanoscale fabrication technologies, the aggravated effects of reliability degradation and variability in process parameters can hinder effective yields. Fortunately, due to the immense flexibility of contemporary reconfigurable hardware (RH), reconfiguration-based resilience can be exploited to effectively tackle such challenges. Nonetheless, reconfiguration-based resiliency is typically limited due to the complexity of the fault resolution space, interconnect routing constraints, and dynamic reconfiguration time in situ. These challenges are addressed herein by deriving a pre-emptive design approach based on union-free hypergraphs, which can define distinct physical implementations with highly separable subsets of the target device's resources covering the largest solution space feasible for reliability exposures and uncertain parametric variations. Two scalable and highly transportable algorithms to realise union-free hypergraphs are introduced and investigated. Hardware demonstration on a commercial-grade field programmable gate array platform shows a significant increase in fault tolerance compared to commonly-used modular redundancy methods. Furthermore, Monte-Carlo statistical results across a set of benchmarks show an average improvement in critical path delay of 6.8, 8.6, and 10.8% for combined variations of 15, 25, and 35%, respectively, while achieving a net reduction in performance variation impact of 34.8, 38, and 41% for identical levels of variability.

Selectively Pseudocompact Groups without Infinite Separable Pseudocompact Subsets

We give a “naive” (i.e., using no additional set-theoretic assumptions beyond ZFC, the Zermelo-Fraenkel axioms of set theory augmented by the Axiom of Choice) example of a Boolean topological group G without infinite separable pseudocompact subsets having the following “selective” compactness property: For each free ultrafilter p on the set N of natural numbers and every sequence ( U n ) of non-empty open subsets of G, one can choose a point x n ∈ U n for all n ∈ N in such a way that the resulting sequence ( x n ) has a p-limit in G; that is, { n ∈ N : x n ∈ V } ∈ p for every neighbourhood V of x in G. In particular, G is selectively pseudocompact (strongly pseudocompact) but not selectively sequentially pseudocompact. This answers a question of Dorantes-Aldama and the first listed author. The group G above is not pseudo- ω -bounded either. Furthermore, we show that the free precompact Boolean group of a topological sum ⨁ i ∈ I X i , where each space X i is either maximal or discrete, contains no infinite separable pseudocompact subsets.

Minor complexity of discrete functions

In this paper we study a class of complexity measures, induced by a new data structure for representing k-valued functions (operations), called minor decision diagram. When assigning values to some variables in a function the resulting functions are called subfunctions, and when identifying some variables the resulting functions are called minors. The sets of essential variables in subfunctions of f are called separable in f.We examine the maximal separable subsets of variables and their conjugates, introduced in the paper, proving that each such set has at least one conjugate. The essential arity gap gap(f) of the function f is the minimal number of essential variables in f which become fictive when identifying distinct essential variables in f. We also investigate separable sets of variables in functions with non-trivial arity gap. This allows us to solve several important algebraic, computational and combinatorial problems about the finite-valued functions.

Antagonistic Control of Social versus Repetitive Self-Grooming Behaviors by Separable Amygdala Neuronal Subsets

Animals display a range of innate social behaviors that play essential roles in survival and reproduction. While the medial amygdala (MeA) has been implicated in prototypic social behaviors such as aggression, the circuit-level mechanisms controlling such behaviors are not well understood. Using cell-type-specific functional manipulations, we find that distinct neuronal populations in the MeA control different social and asocial behaviors. A GABAergic subpopulation promotes aggression and two other social behaviors, while neighboring glutamatergic neurons promote repetitive self-grooming, an asocialbehavior. Moreover, this glutamatergic subpopulation inhibits social interactions independently of its effect to promote self-grooming, while the GABAergic subpopulation inhibits self-grooming, even in a nonsocial context. These data suggest that social versus repetitive asocial behaviors are controlled in an antagonistic manner by inhibitory versus excitatory amygdala subpopulations, respectively. These findings provide a framework for understanding circuit-level mechanisms underlying opponency between innate behaviors, with implications for their perturbation in psychiatric disorders.

A note on the [formula omitted] topology in dual Banach spaces

If X is a Banach space, the γ topology of the dual X∗ is the topology of the uniform convergence on bounded separable subsets of X. We prove, among other things, that co¯(K)=co¯γ(K) for every w∗-compact subset K of X∗. As an application we obtain some new separation results.

Proper forcing axiom and selective separability

We continue the study of Selectively Separable (SS) and, a game-theoretic strengthening, strategically selectively separable spaces (SS +) (see Barman, Dow (2011) [1]). The motivation for studying SS + is that it is a property possessed by all separable subsets of C p ( X ) for each σ-compact space X. We prove that the winning strategy for countable SS + spaces can be chosen to be Markov. We introduce the notion of being compactlike for a collection of open sets in a topological space and with the help of this notion we prove that there are two countable SS + spaces such that the union fails to be SS +, which contrasts the known result about SS spaces. We also prove that the product of two countable SS + spaces is again countable SS +. One of the main results in this paper is that the proper forcing axiom, PFA, implies that the product of two countable Fréchet spaces is SS, a statement that was shown in Barman, Dow (2011) [1] to consistently fail. An auxiliary result is that it is consistent with the negation of CH that all separable Fréchet spaces have π-weight at most ω 1 .

Emerging from the shadows: Follicular helper T cells in autoimmunity

Emerging from the shadows: Follicular helper T cells in autoimmunity

Ultra- [formula omitted]-separability

A metric space X is ultra- m -separable if the weight of the Katětov hull, E ( X ) , of X is no greater than m . It is shown that the collection of all nonempty ultra- m -separable subsets of X is an ideal closed under taking the limit of its members with respect to the Hausdorff distance. As an application of this, it is proved that if ( K , d K ) is precompact and ( X , d X ) is ultra- m -separable, then ( K × X , D ) is ultra- m -separable as well, where D is any metric on K × X such that D ( ( u , x ) , ( u , y ) ) = d X ( x , y ) and D ( ( u , x ) , ( v , x ) ) = d K ( u , v ) for any u , v ∈ K and x , y ∈ X . Bounded ultra- m -separable spaces are characterized by means of their metrically discrete subsets.

Analysis and synthesis of signal classification systems by perturbing pseudoinverse and projection operations

The paper considers the synthesis of signal classification systems using the theory of perturbation of pseudoreverse and projection matrices and proposes an algorithm to select (filter) separable subsets on a finite point set from R n .

Why Sociology is Better Conditioned to Explain Economic Behaviour than Economics

SUMMARYThis note analyzes the impacts of the fragmentation of economics into different schools of thought and of social science into the sub‐disciplines economics, sociology and psychology. Fragmentation is based on the assumption that it is possible to split the set of an individual's behavioural motives into separable and disjoint subsets. However, this assumption runs counter to the insights in psychology. Moreover, even if splitting up were possible, the different subsets of motives finally need to be checked on consistency and weighted so as to obtain a comprehensive description and explanation. Another serious drawback is that specification of empirical models on the basis of one school of thought or one sub‐discipline leads to omitted variables bias and hence biased estimators and tests. Finally, fragmentation may lead to a ‘pick‐and‐mix package’, whereby policy‐makers and politicians feel free to use what suits them. The social rationality model together with the methodological approach prevalent in modern sociology is presented as a framework for integrating the schools of thought in economics and the social science sub‐disciplines.

Separable subspaces of affine function spaces on convex compact sets

Let K be a compact convex subset of a separated locally convex space (over R ) and let A p ( K ) denote the space of all continuous real-valued affine mappings defined on K, endowed with the topology of pointwise convergence on the extreme points of K. In this paper we shall examine some topological properties of A p ( K ) . For example, we shall consider when A p ( K ) is monolithic and when separable compact subsets of A p ( K ) are metrizable.

Two-qubit separability probabilities and Beta functions

Due to recent important work of Zyczkowski and Sommers (quant-ph/0302197 and quant-ph/0304041), exact formulas are available (both in terms of the Hilbert-Schmidt and Bures metrics) for the (n^2-1)-dimensional and (n(n-1)/2-1)-dimensional volumes of the complex and real n x n density matrices. However, no comparable formulas are available for the volumes (and, hence, probabilities) of various separable subsets of them. We seek to clarify this situation for the Hilbert-Schmidt metric for the simplest possible case of n=4, that is, the two-qubit systems. Making use of the density matrix (rho) parameterization of Bloore (J. Phys. A 9, 2059 [1976]), we are able to reduce each of the real and complex volume problems to the calculation of a one-dimensional integral, the single relevant variable being a certain ratio of diagonal entries, nu = (rho_{11} rho_{44})/{rho_{22} rho_{33})$. The associated integrand in each case is the product of a known (highly oscillatory near nu=1) jacobian and a certain unknown univariate function, which our extensive numerical (quasi-Monte Carlo) computations indicate is very closely proportional to an (incomplete) beta function B_{nu}(a,b), with a=1/2, b=sqrt{3}in the real case, and a=2 sqrt{6}/5, b =3/sqrt{2} in the complex case. Assuming the full applicability of these specific incomplete beta functions, we undertake separable volume calculations.

Separable subsets of GFERF negatively curved groups

A word hyperbolic group G is called GFERF if every quasiconvex subgroup coincides with the intersection of finite index subgroups containing it. We show that in any such group, the product of finitely many quasiconvex subgroups is closed in the profinite topology on G.

Codings of separable compact subsets of the first Baire class

Let X be a Polish space and K a separable compact subset of the first Baire class on X . For every sequence f = ( f n ) n dense in K , the descriptive set-theoretic properties of the set L f = { L ∈ [ N ] : ( f n ) n ∈ L is pointwise convergent } are analyzed. It is shown that if K is not first countable, then L f is Π 1 1 -complete. This can also happen even if K is a pre-metric compactum of degree at most two, in the sense of S. Todorčević. However, if K is of degree exactly two, then L f is always Borel. A deep result of G. Debs implies that L f contains a Borel cofinal set and this gives a tree-representation of K . We show that classical ordinal assignments of Baire-1 functions are actually Π 1 1 -ranks on K . We also provide an example of a Σ 1 1 Ramsey-null subset A of [ N ] for which there does not exist a Borel set B ⊇ A such that the difference B ∖ A is Ramsey-null.