Finding Total Unimodularity in Optimization Problems Solved by Linear Programs

A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally unimodular. Still, sometimes it is possible to build an integer solution with the same cost from the fractional solution. Examples are two scheduling problems (Baptiste and Schieber, J. Sched. 6(4):395–404, 2003; Brucker and Kravchenko, J. Sched. 11(4):229–237, 2008) and the single disk prefetching/caching problem (Albers et al., J. ACM 47:969–986, 2000). We show that problems such as the three previously mentioned can be separated into two subproblems: (1) finding an optimal feasible set of slots, and (2) assigning the jobs or pages to the slots. It is straigthforward to show that the latter can be solved greedily. We are able to solve the former with a totally unimodular linear program, from which we obtain simple combinatorial algorithms with improved worst case running time.     

Ultrafast thermal processing and nanocalorimetry at heating and cooling rates up to 1 MK/s

To generate artificial materials with advanced physical and chemical properties and to study phase transition kinetics on submillisecond time scale, an ultrafast nonadiabatic membrane nanocalorimeter was constructed. A set of commercially available membrane gauges for ultrafast nanocalorimetry has been developed. The gauges placed in a thermostat with controlled helium gas pressure and temperature can be utilized as devices for thermal processing and calorimetry with resolution of 1 nJ/K. Controlled ultrafast cooling, as well as heating, up to 10(6) K/s can be attained for nanogram samples. The maximum cooling rate is inversely proportional to the radius of the heated region of the gauge, which was in the range of 10-100 microm depending on the gauge. The minimum addenda heat capacity was 3 nJ/K. The dynamic heat-transfer problem for the temperature distribution in the membrane-gas system at ultrafast processing has been solved. The characteristic rate R(0) corresponding to quasistatic limit of the temperature change in the membrane-gas system has been found to be equal to 10(5) K/s for a 1 microm thick silicon nitride membrane in helium gas. Calorimeter performance at ultrafast rates has been verified by a set of test experiments. The method was applied for thermal processing and calorimetric measurements in a set of linear polymers. It has been established that nearly amorphous polyethylene can be obtained at a cooling rate of 10(6) K/s.     

Dimensional reduction of 3D building models using graph theory and its application in building energy simulation

Since the various people involved in the design process for a building project tend to hold conflicting views, this inevitably leads to a range of disparate models for planning and calculation purposes. In order to interpret the relevant geometrical, topological and semantical data for any given building model, we identify a structural component graph, a graph of room faces, a room graph and a relational object graph as aids and explain algorithms to derive these relations. We start with a building model by transferring its geometrical, topological and semantical data into a volume model, decomposing the latter into a so-called connection model and then extracting all air volume bodies and hulls of the model by means of further decomposition into elementary cyclic connection components. The technique is demonstrated within the scope of building energy simulation by deriving both a dimensionally reduced object model required for setting up a thermal multizone model and a geometrical model for defining single or multiple computational fluid dynamic domains in a building together with incidence matrices correlating these models. The algorithm is basically applicable to any building energy simulation tool.

How Convincing is Mr. Data's Smile: Affective Expressions of Machines

Emotions should play an important role in the design of interfaces because people interact with machines as if they were social actors. This paper presents a literature review on affective expressions through speech, music and body language. It summarizes the quality and quantity of their parameters and successful examples of synthesis. Moreover, a model for the convincingness of affective expressions, based on Fogg and Hsiang Tseng (1999), was developed and tested. The empirical data did not support the original model and therefore this paper proposes a new model, which is based on appropriateness and intensity of the expressions. Furthermore, the experiment investigated if the type of emotion (happiness, sadness, anger, surprise, fear and disgust), knowledge about the source (human or machine), the level of abstraction (natural face, computer rendered face and matrix face) and medium of presentation (visual, audio/visual, audio) of an affective expression influences its convincingness and distinctness. Only the type of emotion and multimedia presentations had an effect on convincingness. The distinctness of an expression depends on the abstraction and the media through which it is presented.     

Local Encoding Transformations for Optimizing OBDD-Representations of Finite State Machines

Ordered binary decision diagrams are the state-of-the-art representation of switching functions. In order to keep the sizes of OBDDs tractable, heuristics and dynamic reordering algorithms are applied to optimize the underlying variable order. When finite state machines are represented by OBDDs the state encoding can be used as an additional optimization parameter. In this paper, we analyze local encoding transformations which can be applied dynamically. First, we investigate the potential of re-encoding techniques. We then propose the use of an XOR-transformation and show why this transformation is most suitable among the set of all encoding transformations. The presented theoretical framework establishes a new optimization technique for OBDDs.     

What is the optimal architecture for visual information routing?

Analyzing the design of networks for visual information routing is an underconstrained problem due to insufficient anatomical and physiological data. We propose here optimality criteria for the design of routing networks. For a very general architecture, we derive the number of routing layers and the fanout that minimize the required neural circuitry. The optimal fanout l is independent of network size, while the number k of layers scales logarithmically (with a prefactor below 1), with the number n of visual resolution units to be routed independently. The results are found to agree with data of the primate visual system.     

Artists portray human faces with the Fourier statistics of complex natural scenes

When artists portray human faces, they generally endow their portraits with properties that render the faces esthetically more pleasing. To obtain insight into the changes introduced by artists, we compared Fourier power spectra in photographs of faces and in portraits by artists. Our analysis was restricted to a large set of monochrome or lightly colored portraits from various Western cultures and revealed a paradoxical result. Although face photographs are not scale-invariant, artists draw human faces with statistical properties that deviate from the face photographs and approximate the scale-invariant, fractal-like properties of complex natural scenes. This result cannot be explained by systematic differences in the complexity of patterns surrounding the faces or by reproduction artifacts. In particular, a moderate change in gamma gradation has little influence on the results. Moreover, the scale-invariant rendering of faces in artists' portraits was found to be independent of cultural variables, such as century of origin or artistic techniques. We suggest that artists have implicit knowledge of image statistics and prefer natural scene statistics (or some other rules associated with them) in their creations. Fractal-like statistics have been demonstrated previously in other forms of visual art and may be a general attribute of esthetic visual stimuli.     

Listener-based analysis of surface importance for acoustic metrics

Acoustic quality in room acoustics is measured by well defined quantities, like definition, which can be derived from simulated impulse response filters or measured values. These take into account the intensity and phase shift of multiple reflections due to a wave front emanating from a sound source. Definition (D50) and clarity (C50) for example correspond to the fraction of the energy received in total to the energy received in the first 50 ms at a certain listener position. Unfortunately, the impulse response measured at a single point does not provide any information about the direction of reflections, and about the reflection surfaces which contribute to this measure. For the visualization of room acoustics, however, this information is very useful since it allows to discover regions with high contribution and provides insight into the influence of all reflecting surfaces to the quality measure. We use the phonon tracing method to calculate the contribution of the reflection surfaces to the impulse response for different listener positions. This data is used to compute importance values for the geometry taking a certain acoustic metric into account. To get a visual insight into the directional aspect, we map the importance to the reflecting surfaces of the geometry. This visualization indicates which parts of the surfaces need to be changed to enhance the chosen acoustic quality measure.We apply our method to the acoustic improvement of a lecture hall by means of enhancing the overall speech comprehensibility (clarity) and evaluate the results using glyphs to visualize the clarity (C50) values at listener positions throughout the room.     

Classification and comparison of ligand-binding sites derived from grid-mapped knowledge-based potentials

We describe the application of knowledge-based potentials implemented in the MOE program to compare the ligand-binding sites of several proteins. The binding probabilities for a polar and a hydrophobic probe are calculated on a grid to allow easy comparison of binding sites of superimposed related proteins. The method is fast and simple enough to simultaneously use structural information of multiple proteins of a target family. The method can be used to rapidly cluster proteins into subfamilies according to the similarity of hydrophobic and polar fields of their ligand-binding sites. Regions of the binding site which are common within a protein family can be identified and analysed for the design of family-targeted libraries or those which differ for improvement of ligand selectivity. The field-based hierarchical clustering is demonstrated for three protein families: the ligand-binding domains of nuclear receptors, the ATP-binding sites of protein kinases and the substrate binding sites of proteases. More detailed comparisons are presented for serine proteases of the chymotrypsin family, for the peroxisome proliferator-activated receptor subfamily of nuclear receptors and for progesterone and androgen receptor. The results are in good accordance with structure-based analysis and highlight important differences of the binding sites, which have been also described in the literature.