Distinguished Subset Research Articles

Two-unitary complex Hadamard matrices of order 36

Abstract A family of two-unitary complex Hadamard matrices (CHMs) of size 36 stemming from a particular matrix is constructed. Every matrix in this orbit remains unitary after operations of partial transpose and reshuffling which makes it a distinguished subset of CHM. It provides a novel solution to the quantum version of the Euler problem, in which each field of the Graeco-Latin square of size six contains a symmetric superposition of all 36 officers with phases being multiples of sixth root of unity. This simplifies previously known solutions as all amplitudes of the superposition are equal and the set of phases consists of six elements only. Multidimensional parameterization allows for more flexibility in a potential experimental realization.

Triangulations of non-archimedean curves, semi-stable reduction, and ramification

Let K be a complete discretely valued field with algebraically closed residue field and let ℭ be a smooth projective and geometrically connected algebraic K-curve of genus g. Assume that g⩾2, so that there exists a minimal finite Galois extension L of K such that ℭ L admits a semi-stable model. In this paper, we study the extension L∣K in terms of the minimal triangulation of C, a distinguished finite subset of the Berkovich analytification C of ℭ. We prove that the least common multiple d of the multiplicities of the points of the minimal triangulation always divides the degree [L:K]. Moreover, in the special case when d is prime to the residue characteristic of K, then we show that d=[L:K], obtaining a new proof of a classical theorem of T. Saito. We then discuss curves with marked points, which allows us to prove analogous results in the case of elliptic curves, whose minimal triangulations we describe in full in the tame case. In the last section, we illustrate through several examples how our results explain the failure of the most natural extensions of Saito’s theorem to the wildly ramified case.

Stone space partitions indexed by a poset

Stone space partitions $\{X_{p}\mid p\in P\}$ satisfying conditions like $\bar{X_{p}}=\bigcup_{q\leqslant p}X_{q}$ for all $p\in P$, where $P$ is a poset or PO system (poset with a distinguished subset), arise naturally in the study both of primitive Boolean algebras and of $\omega$-categorical structures. A key concept for studying such partitions is that of a $p$-trim open set which meets precisely those $X_{q}$ for which $q\geqslant p$; for Stone spaces, this is the topological equivalent of a pseudo-indecomposable set. This paper develops the theory of infinite partitions of Stone spaces indexed by a poset or PO system where the trim sets form a neighbourhood base for the topology. We study the interplay between order properties of the poset/PO system and topological properties of the partition, examine extensions and completions of such partitions, and derive necessary and sufficient conditions on the poset/PO system for the existence of the various types of partition studied. We also identify circumstances in which a second countable Stone space with a trim partition indexed by a given PO system is unique up to homeomorphism, subject to choices on the isolated point structure and boundedness of the partition elements. One corollary of our results is that there is a partition $\{X_{r}\mid r\in[0,1]\}$ of the Cantor set such that $\bar{X_{r}}=\bigcup_{s\leqslant r}X_{s}\text{ for all }r\in[0,1]$.

New aspects of clinical and immunological characteristics in patients with anti-asparaginyl tRNA synthetase (anti-KS) autoantibody.

Anti-asparaginyl tRNA synthetase (anti-KS) antibody is present in patients with interstitial lung disease (ILD) accompanied by polymyositis/dermatomyositis. We examined clinical/immunological features of these patients. Polymyositis/dermatomyositis or ILD patients were screened for autoantibodies, and clinical/immunological data were collected retrospectively. ILD was diagnosed by computed tomography, and clinical/immunological features of anti-KS-positive patients were compared with those of anti-Jo-1-positive patients. Sixteen anti-KS-positive patients [female = 11; male = 5; average age 63.6 years (range, 40-81) years] were diagnosed: seven had ILD, four had clinically amyopathic DM (CADM) and ILD, three had Sjögren's syndrome (SS) and ILD one each had rheumatoid arthritis and ILD, or CADM/SS overlap and ILD. All patients had ILD with chronic onset and clinical course; 11/16 (69%) had nonspecific interstitial pneumonia, and five (31%) had usual interstitial pneumonia pattern. Regarding skin manifestations, 4 (27%) had typical DM rash and 11 (69%) had mechanic's hands. All anti-KS-positive patients had no clinical muscle weakness or serum creatine kinase elevation; 8/16 patients (50%) had sicca symptoms at a significantly high frequency compared with anti-Jo-1-positive patients (50% vs 11%, P = 0.01). Anti-KS-positive patients might form a distinguishable subset closely associated with sicca symptoms, CADM and chronic-type ILD with a relatively favourable prognosis.

On Kato's smoothing effect for a fractional version of the Zakharov-Kuznetsov equation

In this work, we study some regularity properties associated with the initial value problem (IVP)$\begin{align} \left\{ \begin{array}{ll} \partial_{t}u-\partial_{x_{1}}(-\Delta)^{\alpha/2} u+u\partial_{x_{1}}u = 0, \quad 0< \alpha\leq 2, & \\ u(x, 0) = u_{0}(x), \quad x = (x_{1}, x_{2}, \dots, x_{n})\in \mathbb{R}^{n}, \, n\geq 2, \quad t\in\mathbb{R}, & \ \end{array} \right. \end{align}\ \ \ \ \ (1)$where $ (-\Delta)^{\alpha/2} $ denotes the $ n- $dimensional fractional Laplacian.We show that solutions to the IVP (1) with initial data in a suitable Sobolev space exhibit a local smoothing effect in the spatial variable of $ \frac{\alpha}{2} $ derivatives, almost everywhere in time. One of the main difficulties that emerge when trying to obtain this regularizing effect underlies that the operator in consideration is non-local, and the property we are trying to describe is local, so new ideas are required. Nevertheless, to avoid these problems, we use a perturbation argument replacing $ (-\Delta)^{\frac{\alpha}{2}} $ by $ (I-\Delta)^{\frac{\alpha}{2}}, $ that through the use of pseudo-differential calculus allows us to show that solutions become locally smoother by $ \frac{\alpha}{2} $ of a derivative in all spatial directions.As a by-product, we use this particular smoothing effect to show that the extra regularity of the initial data on some distinguished subsets of the Euclidean space is propagated by the flow solution with infinity speed.

Transfusion Patterns during Early Follow-up Predict Overall Survival Independently of IPSS-M in Patients with Myelodysplastic Syndromes

Background: The cumulative red blood cells (RBC) transfusion burden is known to impact outcomes in myelodysplastic syndromes (MDS) but doesn't accurately predict prognosis during the early disease phase. Here we aimed to assess the prognostic value of early changes in transfusion patterns in addition to the recent IPSS-M scoring system. Methods: We gathered diagnostic biobank samples from adult patients (pts) with MDS and registered in the Karolinska Institute's biobank (KI) and the National Swedish MDS Biobank (NB) between 2003-2017 and 2013-2017, respectively. DNA targeted sequencing (152 genes) was performed (Bernard et al., NEJM Evid, 2022). Clinical data was retrieved through pts’ charts (KI) and the Swedish cancer registry (NB). Pts were treated according to Nordic/EU guidelines and most common therapies for lower-risk MDS and higher-risk MDS were erythropoietin and azacytidine, respectively. Transfusion data was obtained from the SCANDAT registry. Pts were followed with regards to RBC transfusion until censored due to death, transformation to acute myeloid leukemia (AML-t), allogenic stem cell transplantation (allo-SCT), or end of follow-up on the 31st of August 2018, whichever occurred first. As per the IWG hematological response criteria for MDS (Platzbecker et al., Blood 2019), transfusion states (TS) were categorized every 4 months (m) as transfusion dependent (TD) or transfusion free (TF) during the past 4 m period. Lower-risk MDS (LR) was defined as IPSS-M very low, low and moderate low, and higher-risk MDS (HR) as IPSS-M very high, high and moderate high at diagnosis (Bernard et al., NEJM Evid, 2022). Landmark analyses of overall survival (OS) were performed with the Kaplan-Meier method for estimating probabilities of OS over time. Multivariable analyses were conducted using Cox proportional hazards model. Results: We gathered a cohort of 688 pts with MDS from KI (n=424) and 33 other clinics in Sweden (NB, n=264). Median age at diagnosis was 74 years (y) old (range 19-93). The male:female ratio in the cohort was 1.4. At diagnosis, 63% of the pts were TF. Out of 646 pts evaluable by the IPSS-M score at diagnosis 54% had LR. Most frequently mutated genes in the cohort were TET2, SF3B1, ASXL1, DNMT3A, RUNX1, TET2, TP53 (66% TP53 multihit), U2AF1, STAG2, ZRSR2. Changes between TS (transitions) preferentially occurred within a year after diagnosis (panel A) with a median time for occurrence of transfusion-related transitions of 1.0 y (range 0.33-8.37). Based on this finding, we assessed whether TS at 8 m landmark impacted prognosis. We observed that there was a significant difference in OS since landmark between TF pts compared with TD pts at landmark 8 m and across IPSS-M categories (panel B). LR pts who were TD at 8 m, had a median OS of 3.2 y (95% CI: 2.2-4.0) versus 6.9 y (95% CI: 5.6-8.9) for LR pts who were TF (P<0.0001). Similarly, median OS was 0.8 y (95% CI: 0.6-1.1) in HR and TD pts while it was 2.4 y (95% CI: 2.1-3.1) in HR and TF pts at landmark 8 m (P<0.0001). Interestingly, OS for LR pts who were TD didn't significantly differ from HR pts who were TF at 8 m. Overall, pts TD at 8 m had more gene mutations compared to TF pts (median 5 [1;13] and 4 [1;16], respectively, P=0.0084). Moreover, studying specific genetic subgroups of MDS, TS at 8 m distinguished subsets of pts with adverse or favorable outcomes within SF3B1-mutated LR pts. In this population, the median OS in pts TF at 8 m was 8.4 y (95% CI: 6.5-13.1) compared to 3.2 y (95% CI: 1.7-4.1) for TD pts (P<0.0001). Next, in multivariable analysis, we found that TD at 8 m significantly impacted OS (HR=2.4 [95% CI: 1.9-3.1]), independently of diagnostic IPSS-M score, age, gender and type of MDS (de novo or therapy-related). Conclusion: TS at landmark 8 m, usually after outcome of first-line treatment was evaluated, appears to be a strong and independent predictor of OS in MDS. These findings are of particular importance for the LR group in which it could discriminate subsets with favorable outcomes from those with adverse prognosis. In addition to the IPSS-M calculation at diagnosis, transfusion dependency could be easily used for prognostic reassessment during follow-up. More generally, these results highlight the need of dynamic outcomes prediction tools and/or validation of current prognostic scores in dynamic settings. Finally, multistate modeling of the dataset is being completed and aims to assess how changes of transfusion patterns over time impact prognosis. Figure 1View largeDownload PPTFigure 1View largeDownload PPT Close modal

Universality of persistence diagrams and the bottleneck and Wasserstein distances

We prove that persistence diagrams with the p-Wasserstein distance is the universal p-subadditive commutative monoid on an underlying metric space with a distinguished subset. This result applies to persistence diagrams, to barcodes, and to multiparameter persistence modules. In addition, the 1-Wasserstein distance satisfies Kantorovich-Rubinstein duality.

Computing Weighted Subset Odd Cycle Transversals in H-free graphs

For the Odd Cycle Transversal problem, the task is to find a small set S of vertices in a graph that intersects every cycle of odd length. The Subset Odd Cycle Transversal problem requires S to intersect only those odd cycles that include a vertex of a distinguished vertex subset T. If we are given weights for the vertices, we ask instead that S has small weight: this is the problem Weighted Subset Odd Cycle Transversal. We prove an almost-complete complexity dichotomy for Weighted Subset Odd Cycle Transversal for graphs that do not contain a graph H as an induced subgraph. In particular, our result shows that the complexities of the weighted and unweighted variant do not align on H-free graphs, just as Papadopoulos and Tzimas showed for Subset Feedback Vertex Set.

COVID-19: On the Disparity in Outcomes Between Military and Civilian Populations.

ABSTRACTIntroductionThe CoronaVirus Disease 2019 (COVID-19) pandemic remains a formidable threat to populations around the world. The U.S. Military, in particular, represents a unique and distinguishable subset of the population, primarily due to the age and gender of active duty personnel. Current investigations have focused on health outcome forecasts for civilian populations, making them of limited value for military planning.Materials and MethodsWe have developed and applied an age-structured susceptible, exposed, infectious, recovered, or dead compartmental model for both civilian and military populations, driven by estimates of the time-dependent reproduction number, R(t), which can be both fit to available data and also forecast future cases, intensive care unit (ICU) patients, and deaths.ResultsWe show that the expected health outcomes for active duty military populations are substantially different than for civilian populations of the same size. Specifically, while the number of cases is not expected to differ dramatically, severity, both in terms of ICU burdens and deaths, is substantially lower.ConclusionsOur results confirm that the burden placed on military health centers will be substantially lower than that for equivalent-sized civilian populations. More practically, the tool we have developed to investigate this (https://q.predsci.com/covid19/) can be used by military health planners to estimate the resources needed in particular locations based on current estimates of the transmission profiles of COVID-19 within the surrounding civilian population in which the military installation is embedded. As this tool continues to be developed, it can be used to assess the likely impact of different intervention strategies, as well as vaccine policies; both for the current pandemic as well as future ones.

Languages of higher-dimensional automata

Abstract We introduce languages of higher-dimensional automata (HDAs) and develop some of their properties. To this end, we define a new category of precubical sets, uniquely naturally isomorphic to the standard one, and introduce a notion of event consistency. HDAs are then finite, labeled, event-consistent precubical sets with distinguished subsets of initial and accepting cells. Their languages are sets of interval orders closed under subsumption; as a major technical step, we expose a bijection between interval orders and a subclass of HDAs. We show that any finite subsumption-closed set of interval orders is the language of an HDA, that languages of HDAs are closed under binary unions and parallel composition, and that bisimilarity implies language equivalence.

Abstract PO-034: Changes in cancer associated fibroblast subsets following angiotensin II type I receptor blocker (ARB) treatment reduces transient hypoxia and radiation resistance

Abstract Poorly oxygenated (hypoxic) tumor cells are resistant to radiation and associated with poor patient outcomes. “Chronically” hypoxic cells develop from limited oxygen diffusion through tumor tissue. Changes in blood vessel perfusion cause fluctuations in oxygen delivery resulting in “transiently” hypoxic cells. Transiently hypoxic cells are often near vasculature and more metastatic than chronically hypoxic cells, identifying transient hypoxia as an important therapeutic target. Angiotensin II receptor (AT1R) type 1 blockers (ARBs) are anti-hypertensive agents with potential anti-fibrotic activity. ARB treatment reduces collagen 1 deposition (Col1) which is thought to occur by targeting AT1R-expressing cancer associated fibroblasts (CAFs) in solid tumors. AT1R signaling is activated through its ligand, angiotensin II (Ang II), which ARBs compete with to inhibit AT1R. It is unclear whether systemic sources of Ang II or localized tumor-derived Ang II contributes to CAF AT1R signaling and collagen deposition. Regardless, ARB-mediated inhibition of Col1 deposition was shown to reduced blood vessel compression and improved perfusion. We recently found that treatment with the ARB telmisartan substantially reduced Col1 deposition, stabilized vascular perfusion, and inhibited the development of transient hypoxia in a human tumor xenograft model. However, it only exhibited a modest reduction in CAF activation. Therefore, we hypothesized that only certain subsets of CAFs are responsible for the development of transient hypoxia in solid tumors, and that AT1R signaling between CAFs and cancer cells may be crucial for initiating the Col1 deposition leading to transient hypoxia development. Recent work by Dr. Mechta-Grigoriou’s group reliably identified four functionally distinct CAF subsets in patient breast and ovarian tumor samples using with a multi-color flow cytometry panel of CAF markers. To distinguish CAF subsets in a murine model, we used a similar flow cytometry panel and indeed, found distinguished subsets of CAFs in various human xenograft murine models. Additionally, we show that crosstalk between cancer cells and cancer associated fibroblasts (CAFs) exists in complementary secretion of Ang II and AT1R by cancer cells and cultured fibroblasts, respectively. This indicates that disruption of this localized Ang II may result in changes in CAF secretion and processing of Col1. We predict that this collaboration of CAFs and tumor cells is responsible for collagen deposition, which leads to blood vessel compression, hypoxia, and reduced radiation response. Citation Format: Che-Min Lee, Brennan J. Wadsworth, Kevin L. Bennewith. Changes in cancer associated fibroblast subsets following angiotensin II type I receptor blocker (ARB) treatment reduces transient hypoxia and radiation resistance [abstract]. In: Proceedings of the AACR Virtual Special Conference on Radiation Science and Medicine; 2021 Mar 2-3. Philadelphia (PA): AACR; Clin Cancer Res 2021;27(8_Suppl):Abstract nr PO-034.

On Self-Mullineux and Self-Conjugate Partitions

The Mullineux involution is a relevant map that appears in the study of the modular representations of the symmetric group and the alternating group. The fixed points of this map are certain partitions of particular interest. It is known that the cardinality of the set of these self-Mullineux partitions is equal to the cardinality of a distinguished subset of self-conjugate partitions. In this work, we give an explicit bijection between the two families of partitions in terms of the Mullineux symbol.

Chimeras and Clusters Emerging from Robust-Chaos Dynamics

We show that dynamical clustering, where a system segregates into distinguishable subsets of synchronized elements, and chimera states, where differentiated subsets of synchronized and desynchronized elements coexist, can emerge in networks of globally coupled robust-chaos oscillators. We describe the collective behavior of a model of globally coupled robust-chaos maps in terms of statistical quantities and characterize clusters, chimera states, synchronization, and incoherence on the space of parameters of the system. We employ the analogy between the local dynamics of a system of globally coupled maps with the response dynamics of a single driven map. We interpret the occurrence of clusters and chimeras in a globally coupled system of robust-chaos maps in terms of windows of periodicity and multistability induced by a drive on the local robust-chaos map. Our results show that robust-chaos dynamics does not limit the formation of cluster and chimera states in networks of coupled systems, as it had been previously conjectured.

Discounted Hamilton-Jacobi equations on networks and asymptotic analysis

We study discounted Hamilton Jacobi equations on networks, without putting any restriction on their geometry. Assuming the Hamiltonians continuous and coercive, we establish a comparison principle and provide representation formulae for solutions. We follow the approach introduced in 11, namely we associate to the differential problem on the network, a discrete functional equation on an abstract underlying graph. We perform some qualitative analysis and single out a distinguished subset of vertices, called lambda Aubry set, which shares some properties of the Aubry set for Eikonal equations on compact manifolds. We finally study the asymptotic behavior of solutions and lambda Aubry sets as the discount factor lambda becomes infinitesimal.

The local structure of the free boundary in the fractional obstacle problem

Abstract Building upon the recent results in [M. Focardi and E. Spadaro, On the measure and the structure of the free boundary of the lower-dimensional obstacle problem, Arch. Ration. Mech. Anal. 230 2018, 1, 125–184] we provide a thorough description of the free boundary for the solutions to the fractional obstacle problem in ℝ n + 1 {\mathbb{R}^{n+1}} with obstacle function φ (suitably smooth and decaying fast at infinity) up to sets of null ℋ n - 1 {{\mathcal{H}}^{n-1}} measure. In particular, if φ is analytic, the problem reduces to the zero obstacle case dealt with in [M. Focardi and E. Spadaro, On the measure and the structure of the free boundary of the lower-dimensional obstacle problem, Arch. Ration. Mech. Anal. 230 2018, 1, 125–184] and therefore we retrieve the same results: (i) local finiteness of the ( n - 1 ) {(n-1)} -dimensional Minkowski content of the free boundary (and thus of its Hausdorff measure), (ii) ℋ n - 1 {{\mathcal{H}}^{n-1}} -rectifiability of the free boundary, (iii) classification of the frequencies and of the blowups up to a set of Hausdorff dimension at most ( n - 2 ) {(n-2)} in the free boundary. Instead, if φ ∈ C k + 1 ⁢ ( ℝ n ) {\varphi\in C^{k+1}(\mathbb{R}^{n})} , k ≥ 2 {k\geq 2} , similar results hold only for distinguished subsets of points in the free boundary where the order of contact of the solution with the obstacle function φ is less than k + 1 {k+1} .

Some Multisecret-Sharing Schemes over Finite Fields

A secret sharing scheme is a method of assigning shares for a secret to some participants such that only some distinguished subsets of these subsets can recover the secret while other subsets cannot. Such schemes can be used for sharing a private key, for digital signatures or sharing the key that can be used to decrypt the content of a file. There are many methods for secret sharing. One of them was developed by Blakley. In this work, we construct a multisecret-sharing scheme over finite fields. The reconstruction algorithm is based on Blakley’s method. We determine the access structure and obtain a perfect and ideal scheme.

On the Number of Biased Graphs

A biased graph is a graph $G$, together with a distinguished subset $\mathcal{B}$ of its cycles, so that no theta-subgraph of $G$ contains precisely two cycles in $\mathcal{B}$. A large number of biased graphs can be constructed by choosing $G$ to be a complete graph, and $\mathcal{B}$ to be an arbitrary subset of its Hamilton cycles. We show that, on the logarithmic scale, the total number of simple biased graphs on $n$ vertices does not asymptotically exceed the number that can be constructed in this elementary way.

Barriers to worldwide institutionalization of social and environmental disclosure

ABSTRACTThis study analyzes how groups of organizations that share their social and environmental information are formed in a similar way to identify barriers to the homogenization of social and environmental disclosure (SED) at the international level. Based on a sample of observations of listed firms from six different countries, results suggest that SED does not homogenize globally, spontaneously, because of cultural and geographical barriers. The institutions of environmental disclosure (ED) and social disclosure (SD) are different, thus forming different organizational fields at the international level. The spoken language is a barrier to the international isomorphism of ED and therefore to its comparability. However, language is a less important barrier to SD. When cultural institutions are weaker or have the same roots as North American institutions, cultural diversity does not stop the homogenization of the SD. Moreover, the ED is more isomorphic/comparable at the global level than SD, while the SD is more isomorphic/comparable at the level of culturally distinguishable subsets than ED.

Local dimensions of random homogeneous self-similar measures: strong separation and finite type

We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the deterministic case. The overlapping case is more complicated; we introduce the notion of finite type for random homogeneous iterated function systems and give a formula for the local dimensions of finite type, regular, random homogeneous self-similar measures in terms of Lyapunov exponents of certain transition matrices. We show that almost all points with respect to this measure are described by a distinguished subset called the essential class, and that the dimension of the support can be computed almost surely from knowledge of this essential class. For a special subcase, that we call commuting, we prove that the set of attainable local dimensions is almost surely a closed interval. Particular examples of such random measures are analyzed in more detail.

A New Approach to Construct Secret Sharing Schemes Based on Field Extensions

Secret sharing has been a subject of study since 1979. It is important that a secret key, passwords, information of the map of a secret place or an important formula must be keptsecret. The main problem is to divide the secret into pieces instead of storing the whole for a secret sharing. A secret sharing scheme is a way of distributing a secret among a nite set of people such that only some distinguished subsets of these subsets can recover the secret. The collection of these special subsets is called the access structure of the scheme.In this paper, we propose a new approach to construct secret sharing schemes based on field extensions.