Sign Symmetry Research Articles

The Dynamics of Debris Disk Creation in Neutron Star Mergers

The detection of GW170817/AT2017gfo inaugurated an era of multimessenger astrophysics, in which gravitational-wave and multiwavelength photon observations complement one another to provide unique insight into astrophysical systems. A broad theoretical consensus exists, in which the photon phenomenology of neutron star mergers largely rests upon the evolution of the small amount of matter left on bound orbits around the black hole or massive neutron star remaining after the merger. Because this accretion disk is far from inflow equilibrium, its subsequent evolution depends very strongly on its initial state, yet very little is known about how this state is determined. Using both snapshot and tracer particle data from a numerical relativity/MHD simulation of an equal-mass neutron star merger that collapses to a black hole, we show how gravitational forces arising in a nonaxisymmetric, dynamical spacetime supplement hydrodynamical effects in shaping the initial structure of the bound debris disk. The work done by hydrodynamical forces is ∼10 times greater than that due to time-dependent gravity. Although gravitational torques prior to remnant relaxation are an order of magnitude larger than hydrodynamical torques, their intrinsic sign symmetry leads to strong cancellation; as a result, hydrodynamical and gravitational torques have a comparable effect. We also show that the debris disk’s initial specific angular momentum distribution is sharply peaked at roughly the specific angular momentum of the merged neutron star’s outer layers, a few r g c, and identify the regulating mechanism.

Relaxations of sign symmetry and the weighted solidarity values

In this paper, we define and study the class of weighted solidarity values. First, we show that the weighted solidarity values are determined by an underlying procedure of sharing marginal contribution. Then, we propose two relaxations of sign symmetry, called sign symmetry for team mates and weak sign symmetry for team mates, that together with efficiency, additivity, and the A-null player property characterize the classes of positively weighted solidarity values and weighted solidarity values, respectively.

Gain–loss and new axiomatizations of the Shapley value

The aim of this paper is to provide new axiomatizations of the Shapley value that generalize previous characterizations. The first characterization employs the gain–loss property, sign differential marginality and the dummy player property. In the second axiomatization, we use the axioms of the gain–loss property, sign symmetry, marginality and the inessential game property. Finally, we introduce the sign marginality property and characterize the Shapley value by combining the property with the other properties.

DNS of the spatiotemporal evolution of the vorticity in (pure) mode B of a circular cylinder’s wake

In the present paper, the spatio-temporal evolution of the vorticity field in the second wake instability, i.e. (pure) mode B is investigated to understand the wake vortex dynamics and sign relationships among the three vorticity components. Direct numerical simulation of the flow past a circular cylinder in the three-dimensional (3D) wake transition is performed, typically at a Reynolds number of 300. According to the time histories of fluid forces and frequency analysis, three different stages are identified. In the fully developed wake (FDW), the spanwise vortex core is almost two-dimensional, while the vortex braid is 3D due to the dominant streamwise interaction. However, streamwise and vertical vorticities owing to the intrinsic 3D instability are already generated first on cylinder surfaces early in the computational transition (CT). The evolution of additional vorticities with the same features as mode B shows that (pure) mode B could already be formed in the late CT. In the FDW, a special sign symmetry of these additional vorticities on the rear surface is observed, which is exactly opposite to that in (pure) mode B. Similarly, the two sign laws found in (pure) mode A are also verified in three typical regions, independent of the Reynolds number, for (pure) mode B. Particularly, the mechanism for the physical origin of streamwise and vertical vortices in the shear layers is the vortex generation on the wall first and then dominant vortex induction just near the wall. The entire process of the formation and shedding of vortices with three components of vorticity is first and completely illustrated. Other characteristics of the evolution of mode B are presented in detail.

A note on sign symmetry for a subclass of efficient, symmetric, and linear values

Symmetry requires that equally productive players should get the same payoff. Sign symmetry is a considerable weakening of symmetry, which requires equally productive players' payoffs to have the same sign. In this note, we apply sign symmetry, as a substitute of symmetry to characterize a subclass of efficient, symmetric, and linear values.

Establishment of belonging of body parts to one or different corpses according to dermatoglyphic signs of the palms

The purpose of the work is to study the possibilities and options for assessing the degree of bilateral symmetry of dermatoglyphic signs of the right and left palms in solving the practical task of forensic medicine in establishing the belonging of body parts to one or different persons. The material of study was fingerprints of 600 palms of 300 people. It was found that the dermatoglyphic signs of the palms are characterized by a high degree of bilateral symmetry. The most consistent with each other on the right and left palms are the rudiments of papillary ridges, ridge counting and the distance between the finger triradiuses. In practical terms, the most informative are the coincidence of values of the characters having an average frequency of occurrence; coincidence of frequent signs have reliable, but low diagnostic significance. It is shown that, using the recommended set of dermatoglyphic signs of the palms, a forensic expert can, with a high degree of certainty, solve the question of whether the parts of body with the palms belong to one or different dead persons. The prospects of further research aimed at improving the technique are considered.

Relaxations of symmetry and the weighted Shapley values

We revisit Kalai and Samet’s (1987) first characterization of the class of weighted Shapley values. While keeping efficiency, additivity, and the null player property from the original characterization of the symmetric Shapley value, they replace symmetry with positivity and partnership consistency. The latter two properties, however, are neither implied by nor related to symmetry. We suggest relaxations of symmetry that together with efficiency, additivity, and the null player property characterize classes of weighted Shapley values. For example, weak sign symmetry requires the payoffs of mutually dependent players to have the same sign. Mutually dependent players are symmetric players whose marginal contributions to coalitions containing neither of them are zero.

Sign symmetry vs symmetry: Young’s characterization of the Shapley value revisited

We revisit Young’s (Young, 1985) characterization of the Shapley value by efficiency, symmetry, and marginality/strong monotonicity. In particular, we suggest a relaxation of symmetry called sign symmetry. While symmetry requires equally productive players to obtain the same payoffs, sign symmetry only requires their payoffs to have the same sign. It turns out that sign symmetry can take the place of symmetry in Young’s characterization.

MULTIPLE TESTING OF SIGN SYMMETRY FOR STOCK RETURN DISTRIBUTIONS

Multiple statistical procedure for testing elliptical model for stock returns distribution is proposed. Sign symmetry conditions are chosen as individual hypotheses for multiple testing. Distribution free uniformly most powerful tests of Neyman structure are constructed for individual hypotheses testing. Associated stepwise multiple testing procedure is applied for the real market data. Numerical experiments shows that hypothesis of elliptical model is rejected. At the same time it is observed that the graph of rejected individual hypotheses has unexpected structure. Namely, this graph is sparse and has a few hubs of high degree. Removing this hubs leads to nonrejection of hypothesis of elliptical model.

Clinical and electrophysiological features of Guillain–Barré syndrome in Iran

We evaluated the clinical and electrophysiological characteristics of 121 consecutive patients admitted with Guillain–Barré syndrome (GBS) to a tertiary referral hospital in Tehran, Iran, from 1997 to 2007. The mean age of patients was 38.9 (standard deviation 19.7) years. The predominant subtype of GBS was the demyelinating form. Miller Fisher syndrome was present in 3.3% of patients. There was no significant seasonal clustering among the three subtypes, but axonal variants tend to occur in summer. In contrast with other subtypes, the majority of patients with acute motor-sensory axonal neuropathy (AMSAN) were female (72.3%). AMSAN patients also had significantly longer hospitalization time (p=0.002) and intensive care unit (ICU) admission (p=0.017), while none of the acute motor axonal neuropathy patients needed ICU admission. Involvement of cranial nerves and symmetry of signs were significantly detected in the demyelinating variant (p=0.021 and p=0.040, respectively). The overall mortality was 3.3%.

Some properties and applications of the Riemann and Green-Hadamard functions for linear second-order hyperbolic equations

We study some properties of the Riemann and Green-Hadamard functions for linear second-order hyperbolic equations of general form. We consider their sign definiteness and symmetry in a certain sense and prove a comparison type theorem. Some applications are presented.

Clinical features in early Parkinson disease and survival.

To examine the association between demographic and clinical features in early Parkinson disease (PD) and length of survival in a multiethnic population. Clinical features within 2 years of diagnosis were determined for an inception cohort established during 1994-1995. Vital status was determined through December 31, 2005. Predictor variables included age at diagnosis, sex, race/ethnicity, as well as clinical subtype (modified tremor dominant, postural instability gait difficulty), symmetry, cognitive impairment, depression, dysphagia, and hallucinations. Cox proportional hazards regression analysis was used to identify factors associated with shorter survival. Kaiser Permanente Medical Care Program, northern California. Five hundred seventy-three men and women with newly diagnosed PD. Three hundred fifty-two participants in the PD cohort (61.4%) had died in the follow-up period. Older age at diagnosis (hazard ratio [HR], 1.1; 95% confidence interval [CI], 1.09-1.12), modified postural instability gait difficulty subtype (HR, 1.8; 95% CI, 1.3-2.7), symmetry of motor signs (HR, 2.0; 95% CI, 1.1-3.7), mild (HR, 1.7; 95% CI, 1.3-2.2) and severe (HR, 2.7; 95% CI, 1.9-3.9) cognitive impairment, dysphagia (HR, 1.4; 95% CI, 1.1-1.9), and hallucinations (HR, 2.1; 95% CI, 1.3-3.2) were associated with increased all-cause mortality, after adjusting for age, sex, and race/ethnicity. None of the other factors altered mortality risk. In an empirical predictive analysis, most previous significant predictors remained associated with shorter survival. Both motor and nonmotor features in early PD predict increased mortality risk, particularly postural instability gait difficulty, cognitive impairment, and hallucinations. These predictors may be useful in clinical practice and when designing clinical trials.

Clinical features and 123I-FP-CIT SPECT imaging in drug-induced parkinsonism and Parkinson’s disease

To determine clinical predictors and accuracy of (123)I-FP-CIT SPECT imaging in the differentiation of drug-induced parkinsonism (DIP) and Parkinson's disease (PD). Several clinical features and (123)I-FP-CIT SPECT images in 32 patients with DIP, 25 patients with PD unmasked by antidopaminergic drugs (PDu) and 22 patients with PD without a previous history of antidopaminergic treatment (PDc) were retrospectively evaluated. DIP and PD shared all clinical features except symmetry of parkinsonian signs which was more frequently observed in patients with DIP (46.9%) than in patients with PDu (16.0%, p<0.05) or PDc (4.5%, p<0.01). Qualitatively (123)I-FP-CIT SPECT images were normal in 29 patients with DIP (90.6%) and abnormal in all patients with PD, and this imaging technique showed high levels of accuracy. DIP and PD are difficult to differentiate based on clinical signs. The precision of clinical diagnosis could be reliably enhanced by (123)I-FP-CIT SPECT imaging.

123I]FP‐CIT SPET imaging in drug‐induced Parkinsonism

We assessed the status of dopamine nerve terminals in patients treated with dopamine receptor blocking agents (DRBAs) who had developed drug-induced parkinsonism (DIP). We performed [(123)I]FP-CIT SPET in 32 consecutive patients who were on DRBAs for at least 6 months and developed extrapyramidal signs. The UPDRS-III was used to assess clinical severity. Twenty-six age- and sex-matched healthy subjects served as control group. Putamen [(123)I]FP-CIT SPET binding was reduced in 14 and normal in the remaining 18 patients. There was no difference between the two groups for age, duration of DRBAs treatment, UPDRS III, tremor, rigidity, and bradykinesia subscores for upper and lower limbs. Conversely, symmetry of parkinsonian signs and presence bucco-linguo-masticatory dyskinesias were more frequent in individuals with normal tracer binding. Imaging of the dopamine transporter may help to identify subjects with DIP secondary to a loss of dopamine nerve terminals.

On sign symmetric circulant matrices

In the last four decades many researchers have studied and analyzed the study of sign symmetry and positivity of principal minors of matrices, since these issues are related to stability. In this work we extend the theory about sign symmetric basic p-circulant permutation and sifted p-circulant matrices. We present and prove sufficient and necessary conditions for P-matrices and necessary conditions for P 2-matrices. Finally we present a class of matrices, where the P 2-matrices are stable.

Instability in nonautocatalytic ionization-recombination processes

Variational analysis of ionization-recombination processes shows that instability in gas- or solid-state plasmas is possible only if the sign symmetry of the Jacobian matrix of the dynamical system is broken. Well-known autocatalytic processes like impact ionization of impurities in semiconductors provide only one of the possible mechanisms achieving this effect. Electron exchange between atoms in metastable states, level inversion in multiply ionized centers, and impact excitation from free electrons or holes are here proved to be good candidates as well, due to the competition between two or more mutually dependent recombination channels. These instability patterns are employed to model photoconduction in a semiconductor suitably doped with a two-level impurity, obtaining a bistable behavior driven either by the light irradiance alone or by the electric field too.

Spectral properties of sign symmetric matrices

Spectral properties of sign symmetric matrices are studied.A criterion for sign symmetry of shifted basic circulant permutation matrices is proven, and is then used to answer the question which complex numbers can serve as eigenvalues of sign symmetric 3 × 3m atrices. The results are applied in the discussion of the eigenvalues of QM-matrices.In particular, it is shown that for every positive integer n there exists a QM-matrix A such that A k is a sign symmetric P -matrix for all k ≤ n, but not all the eigenvalues of A are positive real numbers. The research of the relationship between stability, positivity of principal minors and sign symmetry was motivated by a research problem by Taussky (12) calling for investigation of the common properties of totally positive matrices, nonsingular M - matrices and positive definite matrices. Stability, positivity of principal minors and weak sign symmetry are amongst those common properties. This paper deals with spectral properties of general sign symmetric matrices and of sign symmetric matrices having some additional properties.

Understanding the time dependence of atomic level populations in evolving plasmas

The time dependence of atomic level populations in evolving plasmas is studied using an eigenfunction expansion of the non-LTE rate equations. The work aims to develop understanding without the need for, and as an aid to, numerical solutions. The discussion is mostly limited to linear systems, especially those for optically thin plasmas, but the implicitly non-linear case of non-LTE radiative transfer is briefly discussed. Eigenvalue spectra for typical atomic systems are examined using results compiled by Hearon. Diagonal dominance and sign symmetry of rate matrices show that just one eigenvalue is zero (corresponding to the equilibrium state), that the remaining eigenvalues have negative real parts, and that oscillations, if any, are necessarily damped. Gershgorin's theorems are used to show that many eigenvalues are determined by the radiative lifetimes of certain levels, because of diagonal dominance. With other properties, this demonstrates the existence of both “slow” and “fast” time-scales, where the “slow” evolution is controlled by properties of meta-stable levels. It is shown that, when collisions are present, Rydberg states contribute only “fast” eigenvalues. This justifies use of the quasi-static approximation, in which atoms containing just meta-stable levels can suffice to determine the atomic evolution on time-scales long compared with typical radiative lifetimes. Analytic solutions for two- and three-level atoms are used to examine the basis of earlier intuitive ideas, such as the “ionizing plasma” approximation. The power and limitations of Gershgorin's theorems are examined through examples taken from the solar atmosphere. The methods should help in the planning and interpretation of both experimental and numerical experiments in which atomic evolution is important. While the examples are astrophysical, the methods and results are applicable to plasmas in general.

An experimental method for in vivo analysis of biomechanical asymmetries of the periodontium.

For analysis of the initial tooth movement in vivo, an optical measuring apparatus with a resolution of 0.001 degree for rotation or 0.5 micron for translation respectively has been developed. Its design is described in detail. Because of its high sensitivity it is experimentally feasible to investigate the biomechanical properties of the periodontium under force application and to determine if it makes any difference whether a tooth is rotated mesially or distally out of its neutral position. For that purpose moments with defined time responses are buccally applied to premolars by means of a cardan shaft and the corresponding rotational angle-time characteristics are recorded. As expected, first measurements show sign symmetry for widely spaced teeth. In the case of pronounced anterior crowding, however, asymmetry seems to occur in such a manner that the force system has to overcome a threshold in order to rotate the tooth distally. Additionally, the periodontium may be subject to a sign-dependent rigidity. In all cases, the movement is limited to some degree.

Positivity of principal minors, sign symmetry and stability

The relation between positivity of principal minors, sign symmetry and stability of matrices is studied. It is shown that for sign symmetric matrices, having positive principal minors is equivalent to stability, to D-stability, and to having a positive scaling into a stable matrix. The relation between spectra of matrices some of whose powers have positive principal minors and matrices whose corresponding powers have positive sums of principal minors of each order is studied as well. It is shown that for matrices of order less than 4 these two classes share the same spectra. The relation of these classes and stability is studied, in particular for sign symmetric matrices and for anti-sign symmetric matrices.