Relative Version Research Articles

Optimal Weighted Load Balancing in TCAMs

Traffic splitting is a required functionality in networks, for example for load balancing over multiple paths or among different servers. The capacities of the servers determine the partition by which traffic should be split. A recent approach implements traffic splitting within the ternary content addressable memory (TCAM), which is often available in switches. It is important to reduce the amount of memory allocated for this task since TCAMs are power consuming and are often also required for other tasks such as classification and routing. Previous work showed how to compute the smallest prefix-matching TCAM necessary to implement a given partition exactly. In this paper we solve the more practical case, where at most <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> prefix-matching TCAM rules are available, restricting the ability to implement exactly the desired partition. We give simple and efficient algorithms to find <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> rules that generate a partition closest in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_\infty $ </tex-math></inline-formula> to the desired one. We do the same for a one-sided version of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_\infty $ </tex-math></inline-formula> which equals to the maximum overload on a server and for a relative version of it. We use our algorithms to evaluate how the expected error changes as a function of the number of rules, the number of servers, and the width of the TCAM.

Radicals and idempotents II

Continuing the study of interactions between radical theory and corners, subrings of the form eAe, where e is an idempotent of a ring A, we examine radicals characterized by the presence or absence of idempotents of various types, relative versions of corner-hereditary and corner-strict radicals corresponding to various types of idempotents, and discuss the smallest corner-strict radical class containing a given class.

Characteristics of Sagittal Spinopelvic Alignment Changes After Symptom Relief After Simple Lumbar Decompression.

Sagittal spinopelvic alignment (SSPA) parameters are essential for the diagnosis of adult spinal deformities (ASDs) and their progression. Certain clinical symptoms that occur in patients with lumbar spinal stenosis (LSS) and herniated nucleus pulposus (HNP) may distort the SSPA and mimic ASD. To differentiate SSPA in symptomatic patients from asymptomatic patients within 10 minutes in the standing position. This retrospective cohort study evaluated changes in SSPA after simple lumbar decompression surgery in patients with LSS and HNP. Relative sagittal alignment (RSA), relative pelvic version, relative lumbar lordosis (RLL), Lordosis Distribution Index (LDI), and global alignment and proportion (GAP) values were calculated using the conventional Schwab classification method. First, the preoperative and postoperative SSPA parameters were compared. Second, patients were subgrouped into symptomatic within 10 minutes of standing (SP group) and other symptoms of LSS and HNP as controls. Changes in SSPA parameters after symptom relief after simple lumbar decompression surgery were compared between the two groups. Overall, all SSPA parameters improved after surgery. However, after subgrouping, patients in the control group did not show significant SSPA alterations, except for LDI, whereas patients in the SP group significantly improved in terms of their RSA, RLL, LDI, and GAP values after symptom relief after surgery. Patients with pain on standing within 10 minutes showed significant correction in RSA, RLL, and GAP values after simple lumbar decompression. Therefore, it is important to observe such clinical symptoms to avoid misdiagnosis of ASD.

Topological characteristic factors and independence along arithmetic progressions

In 1994 Glasner studied the topological characteristic factor for minimal systems. It is shown that up to canonically defined proximal extensions, a characteristic family for τd= T × T2 × ⋯ × Td is the family of canonical PI flows of order d − 1. In this paper, we generalize Glasner’s work to the product system of finitely many minimal systems and give its relative version. As applications, we derive several applications related to independence pairs along arithmetic progressions and Δ-transitivity.

Global Alignment and Proportion (GAP) score in asymptomatic individuals: is it universal?

BACKGROUNDThe global alignment and proportion (GAP) score was established based on American and European subjects, which might limit its applicability to the Chinese population due to ethnicity-related difference of sagittal alignment. PURPOSETo analyze the applicability of GAP score in the Chinese population and to investigate the age- and gender-associated differences of spinopelvic and GAP score parameters. STUDY DESIGNA prospective cross-sectional radiographic study. PATIENTS SAMPLEOf 692 asymptomatic Chinese volunteers aged between 20 and 79 prospectively recruited between January 2017 and June 2019, 490 subjects were eventually included in this study. OUTCOME MEASURESThe pelvic incidence (PI), pelvic tilt (PT), sacral slope (SS), L1-S1 lordosis, L4-S1 lordosis, sagittal vertical axis (SVA), T1 pelvic angle (TPA) and global tilt (GT) were measured on lateral X-rays. The GAP scores and its parameters including relative pelvic version (RPV), relative lumbar lordosis (RLL), lordosis distribution index (LDI) and relative spinopelvic alignment (RSA) were calculated for each subject. METHODSSubjects were divided into four groups: Group 1M: male subjects <60 years old; Group 1F: female subjects <60 years old; Group 2M: male subjects ≥60 years old and Group 2F: female subjects ≥60 years old. The GAP scores and categories were determined and compared between groups. The results of sagittal alignment were compared with the previous studies evaluating the normative sagittal alignment in other populations. Univariate linear regression analysis was carried out between pelvic incidence (PI) and sacral slope (SS), lumbar lordosis (LL) and global tilt (GT) in each group. RESULTSThe distributions of GAP categories and the updated Roussouly classification were statistically different from other populations. Significantly different distribution of GAP categories was observed between Group 1M and Group 2M, Group 1F and Group 2F, and Group 1M and Group 1F. Radiographic measurements and GAP parameters were significantly different between Group 1M and Group 2M, and Group 1F and Group 2F. Gender-related difference of parameters was more prominent between Group 1M and Group 1F. Linear relationship of PI with SS, LL and GT were different from the regression models of “ideal” sagittal alignment in GAP score. CONCLUSIONSThe GAP score might be inappropriate in Chinese population due to ethnicity-related alignment difference. Worse feasibility of GAP score was observed in female and old subjects.

Skill ecosystems in the global South: Informality, inequality, and community setting

The concept of ‘skill ecosystems’ considers how contextual and institutional factors shape the acquisition and utilisation of skills. Although initially developed in the global North, there is value in applying this concept in the global South, where large-scale skill development and vocational education reforms are underway, many of which struggle with post-training skill underutilisation. The concept requires modification, however, if it is to be meaningfully applied in the global South. To date, skill ecosystem research has focused on skill utilisation in contexts of formal employment and the institutional actors who support it. In the global South, where most people are employed in the informal sector, a different approach is required, more sensitive to regional power structures and social inequalities. Geographical research on skills can help develop a more dynamic, relational, and power-inflected version of the skill ecosystem concept. Drawing on a short-term longitudinal study of agricultural skills trainings in India, this paper argues a geographically sensitive skill ecosystems perspective helps identify how context shapes the outcomes of skill development programs. To be meaningfully deployed in relation to informal sector work in the global South, however, it must be extended in at least three ways: (1) a different set of institutions and actors must be recognized as comprising the ‘ecosystem,’ particularly those supporting entrepreneurship; (2) the community and family settings in which informal sector work takes place must be recognized; and (3) social inequalities must be considered to promote greater skill utilisation and more equitable outcomes.

Boundaries of relative factor graphs and subgroup classification for automorphisms of free products

Given a countable group $G$ splitting as a free product $G=G_1\ast\dots\ast G_k\ast F_N$, we establish classification results for subgroups of the group $Out(G,\mathcal{F})$ of all outer automorphisms of $G$ that preserve the conjugacy classes of each $G_i$. We show that every finitely generated subgroup $H\subseteq Out(G,\mathcal{F})$ either contains a relatively fully irreducible automorphism, or else it virtually preserves the conjugacy class of a proper free factor relative to the decomposition (the finite generation hypothesis on $H$ can be dropped for $G=F_N$, or more generally when $G$ is toral relatively hyperbolic). In the first case, either $H$ virtually preserves a nonperipheral conjugacy class in $G$, or else $H$ contains an atoroidal automorphism. The key geometric tool to obtain these classification results is a description of the Gromov boundaries of relative versions of the free factor graph $\mathrm{FF}$ and the $\mathcal{Z}$-factor graph $\mathcal{Z}\mathrm{F}$, as spaces of equivalence classes of arational trees (respectively relatively free arational trees). We also identify the loxodromic isometries of $\mathrm{FF}$ with the fully irreducible elements of $Out(G,\mathcal{F})$, and loxodromic isometries of $\mathcal{Z}\mathrm{F}$ with the fully irreducible atoroidal outer automorphisms.

Assessment of the acetabular version in relation to sagittal sacropelvic parameters.

The relationship between acetabular orientation and the sacropelvic parameters is of interest to both hip and spine surgeons as it is increasingly clear disease in one area can affect the other, including the outcome of surgical procedures. The aim of this study was to further clarify the relationship between measures of acetabular orientation and sacropelvic parameters. This study utilized a trauma CT database. A total of 100 scans on adult patients without overt hip or spinal disease were included. Measures of acetabular orientation included the acetabular sagittal angle (ASA) which uses the anterior pelvic plane as a reference and sacroacetabular angle which uses the sacral endplate as a reference (SA); spinopelvic parameters include the pelvic incidence (PI), sacral anatomic orientation (SAO) and pelvic thickness (PTH). Mean age 48.2years (SD 18.0), 62% male. Mean values were: PI 50.5, SAO 50.7, PTH 106.4 mm, ASA-right 62.1, ASA-left 64.0, SA-right 67.2, and SA-left 65.4. There was substantial correlation between PI and SA (r=0.628-0.630) and also between SAO and SA (-0.657 to -0.692). Liner regression determined SA was best predicted by the model: SA=81×SAO+0.36×PI. When using the anterior pelvic plane as a reference to define acetabular orientation, there does not appear to be any significant relationship between the sagittal orientation of the acetabulum and sacropelvic parameters. Using the sacrum as a common point of reference allows some further understanding of the interplay between pelvic parameters and the orientation of the acetabulum.

Bounds on the Heat Transfer Rate via Passive Advection

In heat exchangers, an incompressible fluid is heated initially and cooled at the boundary. The goal is to transfer the heat to the boundary as efficiently as possible. In this paper we study a related steady version of this problem where a steadily stirred fluid is uniformly heated in the interior and cooled on the boundary. For a given large P\'eclet number, how should one stir to minimize some norm of the temperature? This version of the problem was previously studied by Marcotte, Doering et\ al.\ (SIAM Appl.\ Math '18) in a disk, where the authors used matched asymptotics to show that when the P\'eclet number, $\pe$, is sufficiently large one can stir the fluid in a manner that ensures the total heat is $O(1/\pe)$. In this paper we confirm their results with rigorous proofs, and also provide an almost matching lower bound. For simplicity, we work on the infinite strip instead of the unit disk and the proof uses probabilistic techniques.

On the various notions of Poincaré duality pair

We establish a number of foundational results on Poincaré spaces which result in several applications. One application settles an old conjecture of C.T.C. Wall in the affirmative. Another result shows that for any natural number n n , there exists a finite CW pair ( X , Y ) (X,Y) satisfying relative Poincaré duality in dimension n n with the property that Y Y fails to satisfy Poincaré duality. We also prove a relative version of a result of Gottlieb about Poincaré duality and fibrations.

K‐theory of regular compactification bundles

AbstractLet G be a split connected reductive algebraic group. Let be a ‐torsor over a smooth base scheme and X be a regular compactification of G. We describe the Grothendieck ring of the associated fibre bundle , as an algebra over the Grothendieck ring of a canonical toric bundle over a flag bundle over . These are relative versions of the corresponding results on the Grothendieck ring of X in the case when is a point, and generalize the classical results on the Grothendieck rings of projective bundles, toric bundles and flag bundles.

Comparing the effects of semantically related and non-related verb retrieval treatments in persons with aphasia: a single-case study

ABSTRACT Background Differential topographies of body limbs in the brain would be reflected in differential associations of body-related action verbs. This neuroscience hypothesis may have important implications for the verb dissociations in persons with agrammatic aphasia. Aims This study aimed at examining the effects of semantic feature analysis (SFA) on verb retrieval with an innovation based on the theory of the topographical representation of the verb-semantic functional units through distributed neural circuits. The research question concerned the effect of a verb-oriented SFA approach on two sets of semantically related and non-related verbs for Persian-speaking persons with aphasia. Methods and Procedures Two versions of SFA were applied through a single-subject crossover study with A1B1A2B2/A1B2A2B1 design. The first version utilized semantically related verbs by separating hand- and face-related verbs; the other form used semantically non-related verbs. Participants 1 and 2 received treatment with the A1B2A2B1, and participants 3 and 4 received the A1B1A2B2 order. Level, trend, and slope besides D statistic were analyzed for both the treated and untreated verbs. Outcome and Results SFA was generally effective in both versions; however, greater effect sizes were obtained with semantically related verbs (28.58, 33.48, 7.07, 8.16 for the treated and 13.86, 23.09, 4.38, 4.98 for the untreated verbs in the semantically related version; 15.51, 5.72, 1.73, 6.35 for the treated and 6.35, 4.49, 1.63, 1.29 for the untreated verbs in the semantically non-related verbs). Achievement of the accuracy criterion occurred in less time for the semantically related version. Conclusions Semantic-based treatments were useful with verb problems particularly when they were planned to activate allied neural assemblies. The findings of the present study uphold SFA treatment with semantically related verbs.

Gossip, the Common Denominator

Gossip, the Common Denominator

Topology of leaves for minimal laminations by hyperbolic surfaces

We construct minimal laminations by hyperbolic surfaces whose generic leaf is a disk and contain any prescribed family of surfaces and with a precise control of the topologies of the surfaces that appear. The laminations are constructed via towers of finite coverings of surfaces for which we need to develop a relative version of residual finiteness which may be of independent interest. The main step in establishing this relative version of residual finiteness is to obtain finite covers with control on the second systole of the surface, which is done in the Appendix. In a companion paper, the case of other generic leaves is treated.

The Mental Maxwell Relations: A Thermodynamic Allegory for Higher Brain Functions.

The theoretical framework of classical thermodynamics unifies vastly diverse natural phenomena and captures once-elusive effects in concrete terms. Neuroscience confronts equally varied, equally ineffable phenomena in the mental realm, but has yet to unite or to apprehend them rigorously, perhaps due to an insufficient theoretical framework. The terms for mental phenomena, the mental variables, typically used in neuroscience are overly numerous and imprecise. Unlike in thermodynamics or other branches of physics, in neuroscience, there are no core mental variables from which all others formally derive and it is unclear which variables are distinct and which overlap. This may be due to the nature of mental variables themselves. Unlike the variables of physics, perhaps they cannot be interpreted as composites of a small number of axioms. However, it is well worth exploring if they can, as that would allow more parsimonious theories of higher brain function. Here we offer a theoretical exercise in the spirit of the National Institutes of Health Research Domain Criteria (NIH RDoC) Initiative and the Cognitive Atlas Project, which aim to remedy this state of affairs. Imitating classical thermodynamics, we construct a formal framework for mental variables, an extended analogy – an allegory – between mental and thermodynamic quantities. Starting with mental correlates of the physical indefinables length, time, mass or force, and charge, we pursue the allegory up to mental versions of the thermodynamic Maxwell Relations. The Maxwell Relations interrelate the thermodynamic quantities volume, pressure, temperature, and entropy and were chosen since they are easy to derive, yet capable of generating nontrivial, nonobvious predictions. Our “Mental Maxwell Relations” interlink the mental variables consciousness, salience, arousal, and distraction and make nontrivial, nonobvious statements about mental phenomena. The mental system thus constructed is internally consistent, in harmony with introspection, and respects the RDoC criteria of employing only psychologically valid constructs with some evidence of a brain basis. We briefly apply these concepts to the problem of decision-making and sketch how some of them might be tested empirically.

A Study on the Sufficient Conditional and the Necessary Conditional With Chinese and French Participants.

According to the weak version of linguistic relativity, also called the Sapir-Whorf hypothesis, the features of an individual’s native language influence his worldview and perception. We decided to test this hypothesis on the sufficient conditional and the necessary conditional, expressed differently in Chinese and French. In Chinese, connectors for both conditionals exist and are used in everyday life, while there is only a connector for the sufficient conditional in French. A first hypothesis follows from linguistic relativity: for the necessary conditional, better logic performance is expected in Chinese participants rather than French participants. As a second hypothesis, for all participants, we expect performance on the sufficient conditional to be better than on the necessary conditional. Indeed, despite the isomorphism of the two conditionals, they differ in how information is processed for reasoning. We decided to study reasoning under uncertainty as it reflects reality more accurately. To do so, we analyzed the coherence of participants using de Finetti’s theory for deduction under uncertainty. The results of our study show no significant difference in performance between Chinese and French participants, neither on the sufficient conditional nor on the necessary conditional. Thus, our first hypothesis derived from the weak version of linguistic relativity is not confirmed. In contrast, our results confirm the second hypothesis in two out of three inference schemas.

Local entropy via preimage structure

In this paper, local entropy via the preimage structure for noninvertible maps is considered. For a topological dynamical system and its factor, several relative and local versions of preimage entropies with respect to a Borel cover from topological and measure-theoretic viewpoints are introduced and investigated. The relationships among these quantities are discussed, in particular, variational principles (or variational inequalities) are established. Moreover, it is shown that each local version of these relative preimage entropies coincides with its corresponding global version for a system with uniform separation of preimages.

Obstructions to shake sliceness for links

Shake slice generalizes the notion of a slice link, naturally extending the notion of shake slice knots to links. There is also a relative version, shake concordance, that generalizes link concordance. We show that if two links are shake concordant, then their zero surgery manifolds are homology cobordant. Then we give several obstructions to a link being shake slice; for instance, the Arf invariants vanish for both the link and each component. Finally we show that a shake slice link bounds disjoint disks in a homology 4-ball and hence each component is algebraically slice.

The “Black” Side of the Story: History Rewriting in Andrea Levy’s Small Island

The attempt to recover the history of Black people and integrate it into the narratives on Britain has underscored black British writing since the 1990s. Andrea Levy’s novel Small Island retells the British history during and after the Second World War by inscribing the previously marginalized or obliterated stories of the Afro-Caribbean servicemen and the various black-white encounters and interactions. By recuperating the experience of the black diaspora and integrating it into an otherwise homogeneously white British history, Levy participates in the general effort of the black British writers to redefine Britishness to claim a place in it. Thus it helps construct a more inclusive and relational version of British history, challenging and transforming the exclusively-white configuration of Britishness.

Crystals of relative displays and Calabi-Yau threefolds

Displays can be thought of as relative versions of Fontaine's notion of strongly divisible lattice from integral p-adic Hodge theory. In favourable circumstances, the crystalline cohomology of a smooth projective R-scheme X is endowed with a display-structure coming from complexes associated with the relative de Rham-Witt complex WΩX/R• of [LZ04]. In this article, we use the crystal of relative displays of [GL21] to prove a Grothendieck-Messing type result for the deformation theory of Calabi-Yau threefolds.