Strict Partition Research Articles

On the Shifted Littlewood–Richardson Coefficients and the Littlewood–Richardson Coefficients

We give a new interpretation of the shifted Littlewood–Richardson coefficients \(f_{\lambda \mu }^\nu \) (\(\lambda ,\mu ,\nu \) are strict partitions). The coefficients \(g_{\lambda \mu }\) which appear in the decomposition of Schur Q-function \(Q_\lambda \) into the sum of Schur functions \(Q_\lambda = 2^{l(\lambda )}\sum \nolimits _{\mu }g_{\lambda \mu }s_\mu \) can be considered as a special case of \(f_{\lambda \mu }^\nu \) (here \(\lambda \) is a strict partition of length \(l(\lambda )\)). We also give another description for \(g_{\lambda \mu }\) as the cardinal of a subset of a set that counts Littlewood–Richardson coefficients \(c_{\mu ^t\mu }^{{\tilde{\lambda }}}\). This new point of view allows us to establish connections between \(g_{\lambda \mu }\) and \(c_{\mu ^t \mu }^{{\tilde{\lambda }}}\). More precisely, we prove that \(g_{\lambda \mu }=g_{\lambda \mu ^t}\), and \(g_{\lambda \mu } \le c_{\mu ^t\mu }^{{\tilde{\lambda }}}\). We conjecture that \(g_{\lambda \mu }^2 \le c^{{\tilde{\lambda }}}_{\mu ^t\mu }\) and formulate some conjectures on our combinatorial models which would imply this inequality if it is valid.

Virasoro Action on the Q-Functions

A formula for Schur $Q$-functions is presented which describes the action of the Virasoro operators. For a strict partition, we prove a concise formula for $L_{-k}Q_{\lambda}$, where $L_{-k}$ $(k\geq 1)$ is the Virasoro operator.

IMG-Net: inner-cross-modal attentional multigranular network for description-based person re-identification

Given a natural language description, description-based person re-identification aims to retrieve images of the matched person from a large-scale visual database. Due to the existing modality heterogeneity, it is challenging to measure the cross-modal similarity between images and text descriptions. Many of the existing approaches usually utilize a deep-learning model to encode local and global fine-grained features with a strict uniform partition strategy. This breaks the part coherence, making it difficult to capture meaningful information from the within-part and semantic information among body parts. To address this issue, we proposed an inner-cross-modal attentional multigranular network (IMG-Net) to incorporate inner-modal self-attention and cross-modal hard-region attention with the fine-grained model for extracting the multigranular semantic information. Specifically, the inner-modal self-attention module is proposed to address the within-part consistency broken problem using both spatial-wise and channel-wise information. Following it is a multigranular feature extraction module, which is used to extract rich local and global visual and textual features with the help of group normalization (GN). Then a cross-modal hard-region attention module is proposed to obtain the local visual representation and phrase representation. Furthermore, a GN is used instead of batch normalization for the accurate batch statistics estimation. Comprehensive experiments with ablation analysis demonstrate that IMG-Net achieves the state-of-the-art performance on the CUHK-PEDES dataset and outperforms other previous methods significantly.

Pfaffian identities and Virasoro operators

A formula for Schur Q-functions is presented which describes the action of the Virasoro operators. For a strict partition $$\lambda =(\lambda _1,\lambda _2,\ldots ,\lambda _{2m})$$, we show that, for $$k\ge 1$$, $$L_{k}Q_{\lambda } = \sum ^{2m}_{i= 1}(\lambda _i-k)Q_{\lambda -2k\epsilon _i}$$, where $$L_k$$ is the Virasoro operator given as the quadratic form of free bosons. This main formula follows from the Plucker-like bilinear identity of Q-functions as Pfaffians: $$\sum ^{2m}_{i=2}(-1)^{i}\partial _1Q_{\lambda _1,\lambda _i}\partial _1Q_{\lambda _2, \ldots ,\widehat{\lambda _i},\ldots , \lambda _{2m}}=0$$, where $$\partial _1=\partial /\partial t_1$$. This bilinear identity must be explained in geometric words. We conjecture that the Hirota bilinear equations of the KdV hierarchy are derived from this bilinear identity.

Linear versus spin: representation theory of the symmetric groups

We relate the linear asymptotic representation theory of the symmetric groups to its spin counterpart. In particular, we give explicit formulas which express the normalized irreducible spin characters evaluated on a strict partition $\xi$ with analogous normalized linear characters evaluated on the double partition $D(\xi)$. We also relate some natural filtration on the usual (linear) Kerov-Olshanski algebra of polynomial functions on the set of Young diagrams with its spin counterpart. Finally, we give a spin counterpart to Stanley formula for the characters of the symmetric groups.

Exploring malaria vector diversity on the Amazon Frontier

BackgroundDeforestation in the Amazon and the social vulnerability of its settler communities has been associated with increased malaria incidence. The feeding biology of the most important malaria vectors in the region, notably Nyssorhynchus darlingi, compounds efforts to control vectors and reduce transmission of what has become known as “Frontier Malaria”. Exploring Anophelinae mosquito diversity is fundamental to understanding the species responsible for transmission and developing appropriate management and intervention strategies for malaria control in the Amazon River basin.MethodsThis study describes Anophelinae mosquito diversity from settler communities affected by Frontier Malaria in the states of Acre, Amazonas and Rondônia by analysing COI gene data using cluster and tree-based species delimitation approaches.ResultsIn total, 270 specimens from collection sites were sequenced and these were combined with 151 reference (GenBank) sequences in the analysis to assist in species identification. Conservative estimates found that the number of species collected at these sites was between 23 (mPTP partition) and 27 (strict ABGD partition) species, up to 13 of which appeared to be new. Nyssorhynchus triannulatus and Nyssorhynchus braziliensis displayed exceptional levels of intraspecific genetic diversity but there was little to no support for putative species complex status.ConclusionsThis study demonstrates that Anophelinae mosquito diversity continues to be underestimated in poorly sampled areas where frontier malaria is a major public health concern. The findings will help shape future studies of vector incrimination and transmission dynamics in these areas and support efforts to develop more effective vector control and transmission reduction strategies in settler communities in the Amazon River basin.

Word Sense Clustering and Clusterability

Word sense disambiguation and the related field of automated word sense induction traditionally assume that the occurrences of a lemma can be partitioned into senses. But this seems to be a much easier task for some lemmas than others. Our work builds on recent work that proposes describing word meaning in a graded fashion rather than through a strict partition into senses; in this article we argue that not all lemmas may need the more complex graded analysis, depending on their partitionability. Although there is plenty of evidence from previous studies and from the linguistics literature that there is a spectrum of partitionability of word meanings, this is the first attempt to measure the phenomenon and to couple the machine learning literature on clusterability with word usage data used in computational linguistics. We propose to operationalize partitionability as clusterability, a measure of how easy the occurrences of a lemma are to cluster. We test two ways of measuring clusterability: (1) existing measures from the machine learning literature that aim to measure the goodness of optimal k-means clusterings, and (2) the idea that if a lemma is more clusterable, two clusterings based on two different “views” of the same data points will be more congruent. The two views that we use are two different sets of manually constructed lexical substitutes for the target lemma, on the one hand monolingual paraphrases, and on the other hand translations. We apply automatic clustering to the manual annotations. We use manual annotations because we want the representations of the instances that we cluster to be as informative and “clean” as possible. We show that when we control for polysemy, our measures of clusterability tend to correlate with partitionability, in particular some of the type-(1) clusterability measures, and that these measures outperform a baseline that relies on the amount of overlap in a soft clustering.

Ontological Issues in the Life Sciences

In September 2014, the third European Advanced Seminar in the Philosophy of the Life Sciences (EASPLS) took place at The KLI Institute in Klosterneuburg, outside Vienna. The EASPLS meetings are biennial conferences coordinated by a number of major European institutions involved in the philosophy of the life sciences: Egenis, the Centre for the Study of Life Sciences (Exeter); the European School for Molecular Medicine (SEMM, Milan); Department of Health Sciences, University of Milan; the Institut d’Histoire et de Philosophie des Sciences et des Techniques, Universite Paris 1 Pantheon-Sorbonne (IHPST, Paris); the KLI (Klosterneuburg); the Institut Universitaire de Formation des Enseignants (IUFE) and Department of Philosophy, University of Geneva; and the Department of Logic and Philosophy of Science, University of the Basque Country (San Sebastian). This year’s meeting was directed principally by Werner Callebaut (KLI) and Giovanni Boniolo (European Institute of Oncology (IEO), Milan). The seminar focused on ‘‘ontological issues in the life sciences,’’ a theme that deserves some general comment. For much of the twentieth century, and perhaps still to some extent today, the notion that there would be ontological issues in the life sciences might have sounded strange. Ontology has traditionally been conceived as an area of pure philosophy far removed from the concerns and the possible contributions of the empirical sciences. Conversely, it would seem that any issues that might arise in the life sciences should be resolvable from within, rather than calling for philosophical or ontological intervention. This methodological division partly reflects the strict partition between philosophy and science that was embedded in the old positivistic philosophy of science of Carnap, Neurath, and others belonging to the Vienna Circle. Several developments have contributed to the erosion of this In memoriam: Werner Callebaut.

Multi-clustering Gives Robustness to Modules in Networks

Aims/ Objectives: A protein-protein interaction network is considered as a simple indirected graph, weighted or non weighted. A partition of the vertex set, into connected, eventually overlapping, clusters having an edge density larger than the whole graph, is searched. Such a cluster is denoted as a module. The cellular functionality of proteins is predicted from this network decomposition. To improve the prediction quality, we need to evaluate the robustness of these modules. Methodology: We propose a new method which consists in: selecting a non deterministic algorithm for graph partitioning into separate clusters (optimizing a modularity criterion); applying this algorithm several times to generate a set of close partitions;  calculating a consensus partition from this set. Results: This set of partitions permits to evaluate the robustness of any class as the average percentage of partitions joining any protein pair in this class. This robustness function can be applied to compare the consensus partition resulting of this procedure to the usually single partition computed from the graph. Then, we develop a simulation protocol selecting random graphs having a more or less strong community structure. We show that the multi-clustering method provides modules closer to the communities which are more robust than those of a single partition. Finally, we present a simple procedure to extend a strict partition into an overlapping class system, making multi assignment for proteins that could be placed equally into several modules, because their contributions to modularity are similar. - See more at: http://www.sciencedomain.org/abstract.php?iid=567&id=6&aid=5043#sthash.dFAsAweI.dpuf

Progress on precise control of microstructure of Janus materials

Janus materials with two different chemical regions compartmentalized onto the same objects are gaining growing interests. It has become a new hotspot of material research for its anisotropic composition and structure. It is key to develop new methods that can easily and large-scale synthesize Janus materials with tunable morphology, strict chemical composition partition, functional composite partition, and precise control of microstructure. It will support new ideas and measures for the further production and application of Janus materials

Double-π fully scalable model for on-chip spiral inductors

A novel double-π equivalent circuit model for on-chip spiral inductors is presented. A hierarchical structure, similar to that of MOS models is introduced. This enables a strict partition of the geometry scaling in the global model and the model equations in the local model. The major parasitic effects, including the skin effect, the proximity effect, the inductive and capacitive loss in the substrate, and the distributed effect, are analytically calculated with geometric and process parameters in the local-level. As accurate values of the layout and process parameters are difficult to obtain, a set of model parameters is introduced to correct the errors caused by using these given inaccurate layout and process parameters at the local level. Scaling rules are defined to enable the formation of models that describe the behavior of the inductors of a variety of geometric dimensions. A series of asymmetric inductors with different geometries are fabricated on a standard 0.18-μm SiGe BiCMOS process with 100 Ω/cm substrate resistivity to verify the proposed model. Excellent agreement has been obtained between the measured results and the proposed model over a wide frequency range.

Adaptation of TCR Repertoires to Self-Peptides in Regulatory and Nonregulatory CD4+ T Cells

Currently, it is not understood how the specificity of the TCR guides CD4(+) T cells into the conventional lineage (Tconv) vs directing them to become regulatory (Treg) cells defined by the Foxp3 transcription factor. To address this question, we made use of the "Limited" (LTD) mouse, which has a restricted TCR repertoire with a fixed TCRbeta chain and a TCRalpha chain minilocus. The TCR repertoires of Tconv and Treg cells were equally broad, were distinct, yet overlapped significantly, representing a less strict partition than previously seen between CD4 and CD8 T cells. As a group, the CDR3alpha motifs showed a significant trend to higher positive charge in Treg than in Tconv cells. The Tconv and Treg repertoires were both reshaped between thymus and periphery. Reducing the array of peptides presented by MHC class II molecules by introducing the H2-DM(o/o) mutation into the LTD mouse led to parallel shifts in the repertoires of Tconv and Treg cells. In both cases, the CDR3alpha elements were entirely different and strikingly shortened, relative to normal LTD mice. These peculiar sequences conferred reactivity to wild-type MHC class II complexes and were excluded from the normal repertoire, even among Treg cells, indicating that some forms of self-reactivity are incompatible with selection into the Treg lineage. In conclusion, the Treg repertoire is broad, with distinct composition and characteristics, yet significantly overlapping and sharing structural constraints with the repertoire of conventional CD4(+) T cells.

Schubert classes in the equivariant cohomology of the Lagrangian Grassmannian

Let LG n denote the Lagrangian Grassmannian parametrizing maximal isotropic (Lagrangian) subspaces of a fixed symplectic vector space of dimension 2 n. For each strict partition λ = ( λ 1 , … , λ k ) with λ 1 ⩽ n there is a Schubert variety X ( λ ) . Let T denote a maximal torus of the symplectic group acting on LG n . Consider the T-equivariant cohomology of LG n and the T-equivariant fundamental class σ ( λ ) of X ( λ ) . The main result of the present paper is an explicit formula for the restriction of the class σ ( λ ) to any torus fixed point. The formula is written in terms of factorial analogue of the Schur Q-function, introduced by Ivanov. As a corollary to the restriction formula, we obtain an equivariant version of the Giambelli-type formula for LG n . As another consequence of the main result, we obtained a presentation of the ring H T ∗ ( LG n ) .

LITTLEWOOD'S MULTIPLE FORMULA FOR SPIN CHARACTERS OF SYMMETRIC GROUPS

This paper deals with some character values of the symmetric group Sn as well as its double cover ~Sn. Let xλ(p) be the irreducible character of Sn, indexed by the partition λ and evaluated at the conjugacy class p. Comparing the character tables of S2 and S4, one observes that x(4)(2p)=x(2)(p) x(22)(2p)=x(2)(p)+x(1(2))(p) for p = (2), 2p = (4) and p = (12), 2p = (22). A number of such observations lead to what we call Littlewood's multiple formula (Theorem 1.1). This formula appears in Littlewood's book [2]. We include a proof that is based on an `inflation' of the variables in a Schur function. This is different from one given in [2], and we claim that it is more complete than the one given there. Our main objective is to obtain the spin character version of Littlewood's multiple formula (Theorem 2.3). Let ζλ(p) be the irreducible negative character of ~Sn (cf. [1]), indexed by the strict partition λ and evaluated at the conjugacy class p. One finds character tables (ζλ(p)) in [1] for n ≤ 14. This time we evidently see that ζ3λ(3p) = ζλ(p) for λ = (4),(3; 1) and p = (3,1),(14). The proof of Theorem 2.3 is achieved in a way that is similar to the case of ordinary characters. Instead of a Schur function, we deal with Schur's P-function, which is defined as a ratio of Pfaffians.

Stability in coalition formation games

In the context of coalition formation games a player evaluates a partition on the basis of the set she belongs to. For this evaluation to be possible, players are supposed to have preferences over sets to which they could belong. In this paper, we suggest two extensions of preferences over individuals to preferences over sets. For the first one, derived from the most preferred member of a set, it is shown that a strict core partition always exists if the original preferences are strict and a simple algorithm for the computation of one strict core partition is derived. This algorithm turns out to be strategy proof. The second extension, based on the least preferred member of a set, produces solutions very similar to those for the stable roommates problem.

Les services secrets gaullistes à l'épreuve de la politique (1940-1947)

The Politicization of French Intelligence Services: From Military to Political Control (1940-1947) Sébastien Laurent The exceptional military and political events due to the World War II have deeply modified the conditions under which the French intelligence services acted beforehand. The strict partition between military and political fields at the time of the third Republic has to be considered ail over again. The purpose of this article is to analyse the reasons of this drastic upheaval consisting in the intelligence services escaping from the military command. In London, then in Algiers there was a series of conflicts between the inner French Resistance and the de Gaulle's attendants, leading to the foundation of the SDECE (Service de documentation exterieure et de contre-espionnage). Hereafter the intelligence services, linked since 1945 to those of the Presidence du conseil became the aims of hard political struggles in parliamentary circles as in the press of the new regime. The "Passy affair" which occurred in 1946 appeared as a typical example of the new balanced political and journalistic influences from which since then, the secret officers could not escape.

Generalized Hook and Content Numbers Identities—The Projective Case

The study of identities of hook pairs and of content pairs of partitions in is continued. For a strict partition λ= (λ1>⋯>λk) letμ= (λ1,⋯ , λk|λ1− 1,⋯ , λk− 1) in the Frobenius notation. It is proved that for such partitions there are refinements of the identities in , and further identities exist which arise from half of each of the diagrams involved.

Remarks on the Schur—Howe—Sergeev Duality

We establish a new Howe duality between a pair of two queer Lie superalgebras (q(m),q(n)). This gives a representation theoretic interpretation of a well-known combinatorial identity for Schur Q-functions. We further establish the equivalence between this new Howe duality and the Schur–Sergeev duality between q(n) and a central extension \(\tilde H\) of the hyperoctahedral group Hk. We show that the zero-weight space of a q(n)-module with highest weight λ given by a strict partition of n is an irreducible module over the finite group \(\tilde H\) parameterized by λ. We also discuss some consequences of this Howe duality.

An unusually strict product partition of an excited diazirine–carbene system

Photolysis of 3-tert-butyl-3-chlorodiazirine produces 2-chloro-3-methyl-but-2-ene and 2,2-dimethyl-1-chlorocyclopropane; the former stems from 1,2-methyl migration and nitrogen loss in the excited state diazirine, whilst the latter is a product of 1,3-CH insertion in the tert-butylchlorocarbene derived from the diazirine.

Social Grammar for Culture: Reply to Steven Brint

Professor Brint sees my basic point that vacancies reveal structure. Where his interpretation is a bit skewed is that for me vacancies reveal specifically social structure, at middle range, so that they do not provide a general mechanism for revealing cognitive or cultural process. I do see Brint's general point, and indeed I have one book in press and one in manuscript that work exactly toward embedding culture and identity into social structure and its processes of agency, but Brint and I disagree on how to think about embedding. The core idea of blockmodels, which Brint argues are central to my vision of structuralism, is structural equivalence: each set of actors, who are similarly connected (in several types of ties, and through indirect paths as well as by direct ties) with respect to other such sets in a partition, exhibits similar behavior, whether or not much direct connection exists within that set. (Finding the sets is quite a trick, for which John Boyd [1991] provides a definitive mathematical and statistical exposition. He also shows in this exposition that one need not impose a strict partition.) Professor Brint observes, in his second comment (of five), that this approach of mine misses direct impacts from cultural embeddings evinced in attributes of the actors. I should hope so! Did Steven Brint also complain when his English teachers explained grammar, and in particular syntax, separately from the content, be it detective novel or geography? Brint prefers to blockmodel constructs (his note 10). Catnet is a term from an introductory course (Soc Rel 10) that I taught in the 1960s; this term is very useful for stuffing culture in with social form. But I now argue (forthcoming, end of chap. 2) that catnets are found only in contexts without clear social disciplines. The possibility of making just such discriminations was a chief reason for the rigorous abstraction of social structure separately from cultural structure. (This is a reason understood also by the anonymous reviewer quoted by Brint in his note 9.) Brint (in his third comment) complains of a lack of propositions resulting from blockmodels research. Brint himself brilliantly supplies several trial propositions in the two paragraphs following his X-ray metaphor. Other, even more explicitly grammatical propositions come from blockmodeling as role algebra, which was introduced in Boorman and White (1976) and is brought to full mathematical rigor by Boyd (1991). Lorrain and Boorman's First Letter-Last Letter Law (see Boyd 1991) was only the first payoff from these social grammars for culture. Brint slights this algebraic formulation of blockmodeling, which came first and was pursued technically by Bonacich and McConaghy (1979), and Kim and Roush (1978), and from which Breiger and Pattison (1978) derived propositions about elites. Overviews are given by Kim and Roush (1980, 1987) and by Wasserman and Faust (1991). In his fifth comment, Brint bemoans the disappearance of idiographic social science. Surely this is rhetoric, which signals (by analogy to his argument about my rhetoric) that idiography in fact is making a comeback. The political scientist Lucien Pye (1991) provides