a computational proof of complexity of some restricted counting problems

South Central University

The Effect of Indexing on the Complexity of Object Recognition

Many current recognition systems use constrained search to locate objects in cluttered environments. Previous formal analysis has shown that the expected amount of search is quadratic in the number of model and data features, if all the data is known to come from a sinlge object, but is exponential when spurious data is included. If one can group the data into subsets likely to have come from a single object, then terminating the search once a "good enough" interpretation is found reduces the expected search to cubic. Without successful grouping, terminated search is still exponential. These results apply to finding instances of a known object in the data. In this paper, we turn to the problem of selecting models from a library, and examine the combinatorics of determining that a candidate object is not present in the data. We show that the expected search is again exponential, implying that naﶥ approaches to indexing are likely to carry an expensive overhead, since an exponential amount of work is needed to week out each of the incorrect models. The analytic results are shown to be in agreement with empirical data for cluttered object recognition.

On the Complexity of Quantum ACC

For any q > 1, let MOD_q be a quantum gate that determines if the number of 1's in the input is divisible by q. We show that for any q,t > 1, MOD_q is equivalent to MOD_t (up to constant depth). Based on the case q=2, Moore has shown that quantum analogs of AC^(0), ACC[q], and ACC, denoted QAC^(0)_wf, QACC[2], QACC respectively, define the same class of operators, leaving q > 2 as an open question. Our result resolves this question, implying that QAC^(0)_wf = QACC[q] = QACC for all q. We also prove the first upper bounds for QACC in terms of related language classes. We define classes of languages EQACC, NQACC (both for arbitrary complex amplitudes) and BQACC (for rational number amplitudes) and show that they are all contained in TC^(0). To do this, we show that a TC^(0) circuit can keep track of the amplitudes of the state resulting from the application of a QACC operator using a constant width polynomial size tensor sum. In order to accomplish this, we also show that TC^(0) can perform iterated addition and multiplication in certain field extensions.

Mapping the complexity of transcription control in higher eukaryotes.

Recent genomic analyses suggest the importance of combinatorial regulation by broadly expressed transcription factors rather than expression domains characterized by highly specific factors.

Complexity of mixed shop scheduling problems: A survey

We survey recent results on the computational complexity of mixed shop scheduling problems. In a mixed shop, some jobs have fixed machine orders (as in the job shop), while the operations of the other jobs may be processed in arbitrary order (as in the open shop). The main attention is devoted to establishing the boundary between polynomially solvable and NP-hard problems. When the number of operations per job is unlimited, we focus on problems with a fixed number of jobs.

On the complexity of the water-gas shift reaction mechanism over a Pt/CeO2 catalyst: Effect of the temperature on the reactivity of formate surface species studied by operando DRIFT during isotopic transient at chemical steady-state

The present report investigates the role of formate species as potential reaction intermediates for the WGS reaction (CO + H2O -> CO2 + H-2) over a Pt-CeO2 catalyst. A combination of operando techniques, i.e., in situ diffuse reflectance FT-IR (DRIFT) spectroscopy and mass spectrometry (MS) during steady-state isotopic transient kinetic analysis (SSITKA), was used to relate the exchange of the reaction product CO2 to that of surface formate species. The data presented here suggest that a switchover from a non-formate to a formate-based mechanism could take place over a very narrow temperature range (as low as 60 K) over our Pt-CeO2 catalyst. This observation clearly stresses the need to avoid extrapolating conclusions to the case of results obtained under even slightly different experimental conditions. The occurrence of a low-temperature mechanism, possibly redox or Mars van Krevelen-like, that deactivates above 473 K because of ceria over-reduction is suggested as a possible explanation for the switchover, similarly to the case of the CO-NO reaction over Cu, I'd and Rh-CeZrOx (see Kaspar and co-workers [1-3]). (c) 2006 Elsevier B.V. All rights reserved.