Can One Hear a Matrix? Recovering a Real Symmetric Matrix from Its Spectral Data

The spectrum of a real and symmetric $$N\times N$$ N × N matrix determines the matrix up to unitary equivalence. More spectral data is needed together with some sign indicators to remove the unitary ambiguities. In the first part of this work, we specify the spectral and sign information required for a unique reconstruction of general matrices. More specifically, the spectral information consists of the spectra of the N nested main minors of the original matrix of the sizes $$1,2,\ldots ,N$$ 1 , 2 , … , N . However, due to the complicated nature of the required sign data, improvements are needed in order to make the reconstruction procedure feasible. With this in mind, the second part is restricted to banded matrices where the amount of spectral data exceeds the number of the unknown matrix entries. It is shown that one can take advantage of this redundancy to guarantee unique reconstruction of generic matrices; in other words, this subset of matrices is open, dense and of full measure in the set of real, symmetric and banded matrices. It is shown that one can optimize the ratio between redundancy and genericity by using the freedom of choice of the spectral information input. We demonstrate our constructions in detail for pentadiagonal matrices.

ALGORITHM FOR EVALUATING THE QUALITY OF SOFTWARE PRODUCTS

An algorithm for evaluating the quality of software products is proposed, which includes two levels. At the first level, indicators are considered: operational efficiency, memory efficiency, error tolerance, unified communication procedures, data uniformity, traceability, consistency, information input and output speed, robustness, accuracy, access control, redistribution, availability, simplicity, information input and output volume, community, independence from other software, the availability of measuring tools, modularity, machine independence, brevity, access control, communication, informational content, completeness, the possibility of training. Applying the convolution algorithm to indicators of the first level, we can obtain indicators of the second level: efficiency, integrity, ease of use, practicality, evaluation, reliability, mobility, correctness, flexibility, the ability to use in other conditions, the possibility of interaction, security. Applying the convolution algorithm to the indicators of the second level, we can evaluate the quality of software. The convolution algorithm is the sum of indicators with weighting factors. The difference from other algorithms is that the coefficients are not calculated. Coefficients are subject to conditions. Firstly, the discreteness condition, i.e. coefficients can take only discrete values with a predetermined step. Secondly, the normalization condition, i.e. the sum of all the coefficients is equal to one. Thirdly, the priority condition, i.e. all coefficients are arranged in increasing order. Using this algorithm, we obtain several convolution values. The final result of the convolution will be their arithmetic mean. Using this algorithm, you can evaluate the quality of both software products and other products and services. In particular, this algorithm can be applied to assess the quality of educational services, medical services, etc.

Image Accessibility for Screen Reader Users: A Systematic Review And A Road Map

A number of studies have been conducted to improve the accessibility of images using touchscreen devices for screen reader users. In this study, we conducted a systematic review of 33 papers to get a holistic understanding of existing approaches and to suggest a research road map given identified gaps. As a result, we identified types of images, visual information, input device and feedback modalities that were studied for improving image accessibility using touchscreen devices. Findings also revealed that little has studied how to automate the generation of image-related information, and that screen reader users play important roles during the evaluation but the design process. Then we introduce two of our recent studies on the accessibility of artwork and comics, AccessArt and AccessComics respectively. Based on the identified key challenges, we suggest a research agenda for improving image accessibility for screen reader users.

INFORMATION MODEL OF COMPUTER AIDED SYSTEM FOR FORECASTING THE TECHNICAL CONDITION OF UNITS OF LOAD-CARRYING VEHICLES AT AGRICULTURAL ENTERPRISES

This paper discusses an information model of a com-puter aided system of software-algorithmic and information tools for advanced forecasting of the parameters of the technical condition of components and aggregates of a load-carrying vehicleby the results of diagnostics present-ed as hierarchically related sets of the complete set of its components. As components of software-algorithmic and information tools, many of the considered models of load-carrying vehiclesare identified; their components and ag-gregates; parameters of the technical condition of load-carrying vehicles; nominal, current and permissible values of the technical condition parameters without repair; the remaining resource of the technical condition parameter; methods for improving forecasting; the coefficient of curva-ture of the change in the predicted parameter over time; normative and reference information; input operational information; operational calculation/output information; development of control actions; operations for diagnosing units and components of load-carrying vehiclesduring the next maintenance No. 1 and others. This model is applica-ble in the development of a system in the environment of a computer spreadsheet for load-carrying vehiclesthat actu-ally exist on farms.

CaMKII activation triggers persistent formation and segregation of postsynaptic liquid phase

Transient information input to brain leads to persistent changes in synaptic circuit, thereby forming memory engrams. Synapse undergoes coordinated functional and structural changes during this process but how such changes are achieved by its component molecules still largely remain enigmatic. We found that activated CaMKII, the central player of synaptic plasticity, undergoes liquid-liquid phase separation (LLPS) with NMDAR subunit GluN2B. Due to CaMKII autophosphorylation, the condensate stably persists even after Ca2+ is removed. The selective binding of activated CaMKII with GluN2B co-segregates AMPAR/neuroligin (NLGN) into a phase-in-phase assembly. Because postsynaptic NLGN clusters presynaptic neurexin and other active zone proteins thereby increasing the release probability of synaptic vesicles, this ensures efficient synaptic transmission. In this way, Ca2+-induced and persistent formation of LLPS by CaMKII serves as molecular basis of memory by functioning as an activity-dependent crosslinker for postsynaptic proteins and segregating trans-synaptic nanocolumns.

Caregiver Decision-making for School Placement of Children Who are Deaf or Hard of Hearing and Children with Other Disabilities: A Global Perspective

Decision-making is fundamental to everyday modern life (Porter, Creed, Hood, & Ching, 2018; Ranyard & Crozier, 2002). Some decisions require little thought, while others are more complex as options considered do not always lead to clear outcomes (Baron, 2008). Caregivers of children who are deaf or hard of hearing (DHH) are frequently confronted with complex decisions (Marschark, 2018), with the almost universal decision encountered being school enrollment choice. This systematic literature review explores worldwide research on factors effecting the decisionmaking processes of caregivers of children who are DHH when deciding on an educational setting. Three databases were searched and reference lists of identified articles examined, which resulted in a limited number of documents located. To broaden the scope of the review, another search was conducted to include caregivers of children with other disabilities. In all, nine articles were found and analyzed for common themes and sub-themes relevant to the decision-making processes of caregivers when choosing educational settings for their children who are DHH or who have other disabilities. Three broadly grouped themes were identified: child-centered, familial, and school. Five sub-themes were also identified: community inclusion, additional disabilities and wellbeing, complexity of decision-making, information input and flow, and school systems and personnel.

Limitations of the Recall Capabilities in Delay-Based Reservoir Computing Systems

We analyse the memory capacity of a delay-based reservoir computer with a Hopf normal form as nonlinearity and numerically compute the linear as well as the higher order recall capabilities. A possible physical realization could be a laser with external cavity, for which the information is fed via electrical injection. A task-independent quantification of the computational capability of the reservoir system is done via a complete orthonormal set of basis functions. Our results suggest that even for constant readout dimension the total memory capacity is dependent on the ratio between the information input period, also called the clock cycle, and the time delay in the system. Optimal performance is found for a time delay about 1.6 times the clock cycle.