scholarly journals Algebraic conditions and the sparsity of spectrally arbitrary patterns

2021 ◽  
Vol 9 (1) ◽  
pp. 257-274
Author(s):  
Louis Deaett ◽  
Colin Garnett
Keyword(s):  
Major Goal ◽  
Algebraic Condition ◽  
Open Question ◽  
Algebraic Tool ◽  
General Method ◽  
Square Matrix ◽  
Spectrally Arbitrary

Abstract Given a square matrix A, replacing each of its nonzero entries with the symbol * gives its zero-nonzero pattern. Such a pattern is said to be spectrally arbitrary when it carries essentially no information about the eigenvalues of A. A longstanding open question concerns the smallest possible number of nonzero entries in an n × n spectrally arbitrary pattern. The Generalized 2n Conjecture states that, for a pattern that meets an appropriate irreducibility condition, this number is 2n. An example of Shitov shows that this irreducibility is essential; following his technique, we construct a smaller such example. We then develop an appropriate algebraic condition and apply it computationally to show that, for n ≤ 7, the conjecture does hold for ℝ, and that there are essentially only two possible counterexamples over ℂ. Examining these two patterns, we highlight the problem of determining whether or not either is in fact spectrally arbitrary over ℂ. A general method for making this determination for a pattern remains a major goal; we introduce an algebraic tool that may be helpful.

Constructing the three-qudit unextendible product bases with strong nonlocality

2022 ◽  
Author(s):  
Bichen Che ◽  
Zhao Dou ◽  
Xiubo Chen ◽  
Yu Yang ◽  
Li Jian ◽  
...  
Keyword(s):  
Positive Answer ◽  
Quantum Nonlocality ◽  
Rubik's Cube ◽  
The Family ◽  
Rubik’S Cube ◽  
Orthogonal Product ◽  
Open Question ◽  
General Method

Abstract The unextendible product bases (UPB) are interesting members of the family of orthogonal product bases. In this paper, we investigate the construction of 3-qudit UPB with strong nonlocality. First, a UPB set in ${{C}^{3}}\otimes {{C}^{3}}\otimes {{C}^{3}}$ of size 19 is presented based on the Shifts UPB. By mapping the system to a Rubik's Cube, we provide a general method of constructing UPB in ${{C}^{d}}\otimes {{C}^{d}}\otimes {{C}^{d}}$ of size ${{\left(d-1 \right)}^{3}}+2d+5$, whose corresponding Rubik's Cube is composed of four parts. Second, for the more general case where the dimensions of parties are different, we extend the classical tile structure to the 3-qudit system and propose the Tri-tile structure. By means of this structure, a ${{C}^{4}}\otimes {{C}^{4}}\otimes {{C}^{5}}$ system of size 38 is obtained based on a ${{C}^{3}}\otimes {{C}^{3}}\otimes {{C}^{4}}$ system of size 19. Then, we generalize this approach to ${{C}^{{{d}_{1}}}}\otimes {{C}^{{{d}_{2}}}}\otimes {{C}^{{{d}_{3}}}}$ system which also consists of four parts. Our research provides a positive answer to the open question raised in [Halder, et al., PRL, 122, 040403 (2019)], indicating that there do exist UPB that can exhibit strong quantum nonlocality without entanglement.

Mars: was There an Ancient Eden?

1997 ◽  
Vol 161 ◽  
pp. 203-218 ◽  
Author(s):  
Tobias C. Owen
Keyword(s):  
Positive Answer ◽  
Biogenic Elements ◽  
Habitable Zones ◽  
The Face ◽  
The Origin Of Life ◽  
Early Mars ◽  
Favorable Conditions ◽  
Open Question ◽  
Rocky Planets ◽  
Impact Erosion

AbstractThe clear evidence of water erosion on the surface of Mars suggests an early climate much more clement than the present one. Using a model for the origin of inner planet atmospheres by icy planetesimal impact, it is possible to reconstruct the original volatile inventory on Mars, starting from the thin atmosphere we observe today. Evidence for cometary impact can be found in the present abundances and isotope ratios of gases in the atmosphere and in SNC meteorites. If we invoke impact erosion to account for the present excess of129Xe, we predict an early inventory equivalent to at least 7.5 bars of CO2. This reservoir of volatiles is adequate to produce a substantial greenhouse effect, provided there is some small addition of SO2(volcanoes) or reduced gases (cometary impact). Thus it seems likely that conditions on early Mars were suitable for the origin of life – biogenic elements and liquid water were present at favorable conditions of pressure and temperature. Whether life began on Mars remains an open question, receiving hints of a positive answer from recent work on one of the Martian meteorites. The implications for habitable zones around other stars include the need to have rocky planets with sufficient mass to preserve atmospheres in the face of intensive early bombardment.

A General Method for Spectrometer Design in the Scoff Approximation

1976 ◽  
Vol 34 ◽  
pp. 538-539
Author(s):  
J. R. Fields
Keyword(s):  
Electron Microscope ◽  
Transmission Electron Microscope ◽  
Energy Analysis ◽  
Incident Beam ◽  
Scanning Transmission Electron Microscope ◽  
Chemical Identification ◽  
Scanning Transmission Electron ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
General Method

The energy analysis of electrons scattered by a specimen in a scanning transmission electron microscope can improve contrast as well as aid in chemical identification. In so far as energy analysis is useful, one would like to be able to design a spectrometer which is tailored to his particular needs. In our own case, we require a spectrometer which will accept a parallel incident beam and which will focus the electrons in both the median and perpendicular planes. In addition, since we intend to follow the spectrometer by a detector array rather than a single energy selecting slit, we need as great a dispersion as possible. Therefore, we would like to follow our spectrometer by a magnifying lens. Consequently, the line along which electrons of varying energy are dispersed must be normal to the direction of the central ray at the spectrometer exit.

Phase behavior of cationic and anionic surfactants at low concentrations

1992 ◽  
Vol 50 (1) ◽  
pp. 694-695
Author(s):  
E. Naranjo
Keyword(s):  
Phase Behavior ◽  
Structural Characterization ◽  
Dynamic Systems ◽  
Anionic Surfactants ◽  
Intermolecular Forces ◽  
Stable Form ◽  
Surfactant Mixtures ◽  
Low Concentrations ◽  
Cationic And Anionic Surfactants ◽  
General Method

Equilibrium vesicles, those which are the stable form of aggregation and form spontaneously on mixing surfactant with water, have never been demonstrated in single component bilayers and only rarely in lipid or surfactant mixtures. Designing a simple and general method for producing spontaneous and stable vesicles depends on a better understanding of the thermodynamics of aggregation, the interplay of intermolecular forces in surfactants, and an efficient way of doing structural characterization in dynamic systems.

Freeze-fracture cytochemistry: A goal set by Russell Steere in 1957

1993 ◽  
Vol 51 ◽  
pp. 60-61
Author(s):  
Nicholas J Severs
Keyword(s):  
Chemical Nature ◽  
Biological Systems ◽  
Freeze Fracture ◽  
Structural Components ◽  
Major Goal ◽  
Membrane Biology ◽  
Routine Application ◽  
The Future ◽  
Freeze Etching

In his pioneering demonstration of the potential of freeze-etching in biological systems, Russell Steere assessed the future promise and limitations of the technique with remarkable foresight. Item 2 in his list of inherent difficulties as they then stood stated “The chemical nature of the objects seen in the replica cannot be determined”. This defined a major goal for practitioners of freeze-fracture which, for more than a decade, seemed unattainable. It was not until the introduction of the label-fracture-etch technique in the early 1970s that the mould was broken, and not until the following decade that the full scope of modern freeze-fracture cytochemistry took shape. The culmination of these developments in the 1990s now equips the researcher with a set of effective techniques for routine application in cell and membrane biology.Freeze-fracture cytochemical techniques are all designed to provide information on the chemical nature of structural components revealed by freeze-fracture, but differ in how this is achieved, in precisely what type of information is obtained, and in which types of specimen can be studied.

On the Semantic Content of Grammatical Gender and Its Impact on the Representation of Human Referents

2010 ◽  
Vol 57 (5) ◽  
pp. 367-375 ◽  
Author(s):  
Lisa Irmen ◽  
Julia Kurovskaja
Keyword(s):  
Semantic Content ◽  
Grammatical Gender ◽  
Differential Effects ◽  
Gender Information ◽  
Masculine Role ◽  
Feminine Role ◽  
And Gender ◽  
Gender Categories ◽  
Open Question

Grammatical gender has been shown to provide natural gender information about human referents. However, due to formal and conceptual differences between masculine and feminine forms, it remains an open question whether these gender categories influence the processing of person information to the same degree. Experiment 1 compared the semantic content of masculine and feminine grammatical gender by combining masculine and feminine role names with either gender congruent or incongruent referents (e.g., Dieser Lehrer [masc.]/Diese Lehrerin [fem.] ist mein Mann/meine Frau; This teacher is my husband/my wife). Participants rated sentences in terms of correctness and customariness. In Experiment 2, in addition to ratings reading times were recorded to assess processing more directly. Both experiments were run in German. Sentences with grammatically feminine role names and gender incongruent referents were rated as less correct and less customary than those with masculine forms and incongruent referents. Combining a masculine role name with an incongruent referent slowed down reading to a greater extent than combining a feminine role name with an incongruent referent. Results thus specify the differential effects of masculine and feminine grammatical gender in denoting human referents.

Caricaturing as a general method to improve poor face recognition: Evidence from low-resolution images, other-race faces, and older adults.

2019 ◽  
Vol 25 (2) ◽  
pp. 256-279 ◽  
Author(s):  
Amy Dawel ◽  
Tsz Ying Wong ◽  
Jodie McMorrow ◽  
Callin Ivanovici ◽  
Xuming He ◽  
...  
Keyword(s):  
Older Adults ◽  
Face Recognition ◽  
Low Resolution ◽  
General Method ◽  
Low Resolution Images

Morphosemantic Analysis and Translation of Medical Compound Terms

1991 ◽  
Vol 30 (01) ◽  
pp. 30-35 ◽  
Author(s):  
P. Dujols ◽  
P. Aubas ◽  
C. Baylon ◽  
F. Grémy
Keyword(s):  
Medical Terms ◽  
General Method

This paper describes an automatic procedure for morphosemantic analysis and translation of compound medical terms. This analysis is of interest for the automatic indexation of medical discharge reports and summaries. Since words with the suffix -osis may have many different semantic interpretations, such -osis forms are taken as examples for a general method that avoids the difficulties in interpreting medical terms as reported in other studies.

Die Europäische Union: eine neue Supermacht mit imperialen Ambitionen?

2005 ◽  
Vol 35 (139) ◽  
pp. 247-266 ◽  
Author(s):  
Hans-Jürgen Bieling
Keyword(s):  
World War Ii ◽  
Economic Crisis ◽  
Europäische Union ◽  
World War ◽  
Political Sovereignty ◽  
Military Conflicts ◽  
Imperial Power ◽  
International Role ◽  
Open Question ◽  
The Eu

Recent theoretical conceptions of imperialism may be useful correctives against idealising and harmonising views of international interdependency and co-operation. Analytically, however, they are not necessarily helpful. In terms of the EU, they do not really comprehend its particular international role. Despite improved financial and military capacities, the EU represents not yet an imperial power. Instead, it still pursues a rather hegemonic foreign policy approach due to internal economic restrictions, fragmented political sovereignty and the historical experiences of beneficial economic and political co-operation after World War II. Eventually, however, it remains an open question, whether the multilateralist, law-based and co-operative posture of the EU will prevail even under conditions of economic crisis and further military conflicts in the adjacent neighbourhood.

Sign in / Sign up

Export Citation Format

Share Document