Counting 1-factors in infinite graphs

F. Bry (J. Combin. Theory Ser. B 34 (1983), 48–57) proved that a locally finite infinite n-connected factorizable graph has at least (n−1)! 1-factors and showed that for n = 2 this lower bound is sharp. We prove that for n≥3 any infinite n-connected factorizable graph has at least n! 1-factors (which is a sharp lower bound).     

The COLUMBUS Standard Integral File Structure: A proposed interchange format

The integral file structure used in the COLUMBUS Program System is described. This file structure is proposed for use as an interchange format for the exchange of information between various electronic structure codes. Access to the integral and density matrix arrays stored in the file structure is simplified by a supporting subroutine library. This library is portable across various computers and is readily available to programmers from the COLUMBUS distribution files. This library provides for the efficient processing of individual records, including the use of asynchronous I/O and the vectorized processing of packed orbital labels. The individual arrays are identified in a self-defining and extensible manner, allowing for the addition of new integral types as demanded by the application. The format of the individual records is also self-defining, allowing for the use of various packing and data compression methods within each record without burdening the calling program with unnecessary complications.     

The DTX-240D digital circuit multiplication system

This paper describes the DTX-240D digital circuit multiplication system (DCMS) offered by ECI Telecom. It will accept up to 240 × 64 kb/s trunks carrying either 64 kb/s voice, voice band analogue non-speech signals, or digital data for transmission over a 2·048 Mb/s digital link. Over 1000 are currently ‘on-line’ and carrying traffic. The system comprises a pair of terminals, one on each side of the interterminal digital link (bearer). It will normally operate in the network at a concentration ratio of 5:1, in which case 150 × 64 kb/s trunks, carrying voice, voice band data or digital data can be concentrated into one 2·048 Mb/s bearer. The users are able to increase the number of trunks up to 240 per 2·048 Mb/s bearer, when time zone differences cause a spread of busy-hour traffic carried on a single system. Each terminal will normally be located at an international switching centre (ISC) but may also be located at an earth-station. The system uses a DSI (digital speech interpolation) stage providing a 2·5:1 multiplication, followed by an additional 2:1 multiplication by means of ADPCM (adaptive differential pulse code modulation). In addition, the VBR (variable bit rate) technique is used to prevent clipping, due to overload congestion. The system can also be used with 1·544 Mb/s digital bit streams (trunk side or bearer).     

Mobile Commerce: Framework,Applications and Networking Support

Advances in e-commerce have resulted in significant progress towards strategies, requirements, and development of e-commerce applications. However, nearly all e-commerce applications envisioned and developed so far assume fixed or stationary users with wired infrastructure. We envision many new e-commerce applications that will be possible and significantly benefit from emerging wireless and mobile networks. To allow designers, developers, and researchers to strategize and create mobile commerce applications, we propose a four-level integrated framework for mobile commerce. Since there are potentially an unlimited number of mobile commerce applications, we attempt to identify several important classes of applications such as mobile financial applications, mobile inventory management, proactive service management, product location and search, and wireless re-engineering. We discuss how to successfully define, architect, and implement the necessary hardware/software infrastructure in support of mobile commerce. Also, to make mobile commerce applications a reality, we address networking requirements, discuss support from wireless carriers, and present some open research problems.     

The Separation and Quantitation of Peptides with and without Oxidation of Methionine and Deamidation of Asparagine Using Hydrophilic Interaction Liquid Chromatography with Mass Spectrometry (HILIC-MS)

Peptides with deamidated asparagine residues and oxidized methionine residues are often not resolved sufficiently to allow quantitation of their native and modified forms using reversed phase (RP) chromatography. The accurate quantitation of these modifications is vital in protein biotherapeutic analysis because they can affect a protein’s function, activity, and stability. We demonstrate here that hydrophilic interaction liquid chromatography (HILIC) adequately and predictably separates peptides with these modifications from their native counterparts. Furthermore, coefficients describing the extent of the hydrophilicity of these modifications have been derived and were incorporated into a previously made peptide retention prediction model that is capable of predicting the retention times of peptides with and without these modifications.

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Graphical Abstract ?

     

Constructing near spanning trees with few local inspections

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded‐degree graph. Given an edge e in G we would like to decide whether e belongs to a connected subgraph consisting of edges (for a prespecified constant ), where the decision for different edges should be consistent with the same subgraph . Can this task be performed by inspecting only a constant number of edges in G ? Our main results are:

• We show that if every t‐vertex subgraph of G has expansion then one can (deterministically) construct a sparse spanning subgraph of G using few inspections. To this end we analyze a “local” version of a famous minimum‐weight spanning tree algorithm.
• We show that the above expansion requirement is sharp even when allowing randomization. To this end we construct a family of 3‐regular graphs of high girth, in which every t‐vertex subgraph has expansion . We prove that for this family of graphs, any local algorithm for the sparse spanning graph problem requires inspecting a number of edges which is proportional to the girth.

© 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 183–200, 2017     

Evaluation of direct analysis in real time mass spectrometry for onsite monitoring of batch slurry reactions

Batch slurry reactions are widely used in the industrial manufacturing of chemicals, pharmaceuticals, petrochemicals and polymers. However, onsite monitoring of batch slurry reactions is still not feasible in production plants due to the challenge in analyzing heterogeneous samples without complicated sample preparation procedures. In this study, direct analysis in real time mass spectrometry (DART-MS) has been evaluated for the onsite monitoring of a model batch slurry reaction. The results suggested that automation of the sampling process of DART-MS is important to achieve quantitative results. With a sampling technique of manual sample deposition on melting point capillaries followed by automatic sample introduction across the helium beam, relative standard deviation (RSD) of the protonated molecule signals from the reaction product of the model batch slurry reaction ranged from 6 to 30%. This RSD range is improved greatly over a sampling technique of manual sample deposition followed by manual sample introduction where the RSDs are up to 110%. Furthermore, with the semi-automated sampling approach, semi-quantitative analysis of slurry samples has been achieved. Better quantification is expected with a fully automated sampling approach.     

The Max-Flow Min-Cut theorem for countable networks

We prove a strong version of the Max-Flow Min-Cut theorem for countable networks, namely that in every such network there exist a flow and a cut that are “orthogonal” to each other, in the sense that the flow saturates the cut and is zero on the reverse cut. If the network does not contain infinite trails then this flow can be chosen to be mundane, i.e. to be a sum of flows along finite paths. We show that in the presence of infinite trails there may be no orthogonal pair of a cut and a mundane flow. We finally show that for locally finite networks there is an orthogonal pair of a cut and a flow that satisfies Kirchhoff's first law also for ends.