New data on shoreline displacement and archaeological chronology in Southern Ostrobothnia and Northern Satakunta

Shoreline displacement in southern Ostrobothnia (Pohjanmaa) and northern Satakunta was studied by using recent sediment, pollen and diatom data supplemented by radiocarbon dates from 12 lake basins at various altitudes that were successively cut off from the Baltic. The shoreline displacement shows a very rapid regression of more than 100 m from deglaciation to about 8000 B.P. after which a distinct retardation took place. Two new stratigraphical Litorina sites, Lake Kalliojärvi (47.7 m) and Lake Tuorilampi (29.3 m a.s.l.) are reported here to supplement the earlier results. The stratigraphy of Tuorilampi shows a possible transregression around 3000 B.P., but the topographic reconstruction suggests a river estuary situation at that time. The Stone Age coastal dwelling places from southern Ostrobothnia are dated with this shore displacement curve on the basis of their altitudes, and the chronology of different stylistic phases from the Mesoliticum to the Late Sub-Neolithic Kiukainen culture is thus obtained. The results are in accordance with the chronology obtained earlier by the time/gradient method. There are, however, some overlapping dates at Middle and Late Comb Ware sites

Spectrum of bound fermion states on vortices in 3^3He-B

We study subgap spectra of fermions localized within vortex cores in $^3$He-B. We develop an analytical treatment of the low-energy states and consider the characteristic properties of fermion spectra for different types of vortices. Due to the removed spin degeneracy the spectra of all singly quantized vortices consist of two different anomalous branches crossing the Fermi level. For singular $o$ and $u$ vortices the anomalous branches are similar to the standard Caroli-de Gennes -Matricon ones and intersect the Fermi level at zero angular momentum yet with different slopes corresponding to different spin states. On the contrary the spectral branches of nonsingular vortices intersect the Fermi level at finite angular momenta which leads to the appearance of a large number of zero modes, i.e. energy states at the Fermi level. Considering the $v$, $w$ and $uvw$ vortices with superfluid cores we show that the number of zero modes is proportional to the size of the vortex core.Comment: 6 pages, 1 figur

Collective Oscillations of Vortex Lattices in Rotating Bose-Einstein Condensates

The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates (BEC) by solving the Bogoliubov-de Gennes (BdG) equation, yielding, e.g., the Tkachenko mode recently observed at JILA. The totally symmetric subset of these modes includes the transverse shear, common longitudinal, and differential longitudinal modes. We also solve the time-dependent Gross-Pitaevskii (TDGP) equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both the BdG and TDGP approaches allows one to unambiguously identify every observed mode.Comment: 5 pages, 4 figure

Mutation of Directed Graphs -- Corresponding Regular Expressions and Complexity of Their Generation

Directed graphs (DG), interpreted as state transition diagrams, are traditionally used to represent finite-state automata (FSA). In the context of formal languages, both FSA and regular expressions (RE) are equivalent in that they accept and generate, respectively, type-3 (regular) languages. Based on our previous work, this paper analyzes effects of graph manipulations on corresponding RE. In this present, starting stage we assume that the DG under consideration contains no cycles. Graph manipulation is performed by deleting or inserting of nodes or arcs. Combined and/or multiple application of these basic operators enable a great variety of transformations of DG (and corresponding RE) that can be seen as mutants of the original DG (and corresponding RE). DG are popular for modeling complex systems; however they easily become intractable if the system under consideration is complex and/or large. In such situations, we propose to switch to corresponding RE in order to benefit from their compact format for modeling and algebraic operations for analysis. The results of the study are of great potential interest to mutation testing

On the effect of variable identification on the essential arity of functions

We show that every function of several variables on a finite set of k elements with n>k essential variables has a variable identification minor with at least n-k essential variables. This is a generalization of a theorem of Salomaa on the essential variables of Boolean functions. We also strengthen Salomaa's theorem by characterizing all the Boolean functions f having a variable identification minor that has just one essential variable less than f.Comment: 10 page

Symmetric Groups and Quotient Complexity of Boolean Operations

The quotient complexity of a regular language L is the number of left quotients of L, which is the same as the state complexity of L. Suppose that L and L' are binary regular languages with quotient complexities m and n, and that the transition semigroups of the minimal deterministic automata accepting L and L' are the symmetric groups S_m and S_n of degrees m and n, respectively. Denote by o any binary boolean operation that is not a constant and not a function of one argument only. For m,n >= 2 with (m,n) not in {(2,2),(3,4),(4,3),(4,4)} we prove that the quotient complexity of LoL' is mn if and only either (a) m is not equal to n or (b) m=n and the bases (ordered pairs of generators) of S_m and S_n are not conjugate. For (m,n)\in {(2,2),(3,4),(4,3),(4,4)} we give examples to show that this need not hold. In proving these results we generalize the notion of uniform minimality to direct products of automata. We also establish a non-trivial connection between complexity of boolean operations and group theory

Vortex core transitions in superfluid 3He in globally anisotropic aerogels

Core structures of a single vortex in A-like and B-like phases of superfluid 3He in uniaxially compressed and stretched aerogels are studied by numerically solving Ginzburg-Landau equations derived microscopically. It is found that, although any uniaxial deformation leads to a wider A-like phase with the axial pairing in the pressure-temperature phase diagram, the vortex core states in the two phases in aerogel depend highly on the type of deformation. In a compressed aerogel, the first-order vortex core transition (VCT) previously seen in the bulk B phase appears at any pressure in the B-like phase while no strange vortex core is expected in the corresponding A-like phase. By contrast, in a stretched aerogel, the VCT in the B-like phase is lost while another VCT is expected to occur between a nonunitary core and a polar one in the A-like phase. Experimental search for these results is hoped to understand correlation between superfluid 3He and aerogel structure.Comment: 7 pages, 6 figures Text was changed. Resubmitted versio

Quantum circuits with uniformly controlled one-qubit gates

Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit gates and a single diagonal n-qubit gate. The circuit is based on the so-called quantum multiplexor, for which we provide a modified construction. We illustrate the versatility of these gates by applying them to the decomposition of a general n-qubit gate and a local state preparation procedure. Moreover, we study their implementation using only nearest-neighbor gates. We give upper bounds for the one-qubit and controlled-NOT gate counts for all the aforementioned applications. In all four cases, the proposed circuit topologies either improve on or achieve the previously reported upper bounds for the gate counts. Thus, they provide the most efficient method for general gate decompositions currently known.Comment: 8 pages, 10 figures. v2 has simpler notation and sharpens some result

Half-Quantum Vortices in Thin Film of Superfluid 3^3He

Stability of a half-quantum vortex (HQV) in superfluid $^3$He has been discussed recently by Kawakami, Tsutsumi and Machida in Phys. Rev. B {\bf 79}, 092506 (2009). We further extend this work here and consider the A$_2$ phase of superfluid $^3$He confined in thin slab geometry and analyze the HQV realized in this setting. Solutions of HQV and singly quantized singular vortex are evaluated numerically by solving the Ginzburg-Landau (GL) equation and respective first critical angular velocities are obtained by employing these solutions. We show that the HQV in the A$_2$ phase is stable near the boundary between the A$_2$ and A$_1$ phases. It is found that temperature and magnetic field must be fixed first in the stable region and subsequently the angular velocity of the system should be increased from zero to a sufficiently large value to create a HQV with sufficiently large probability. A HQV does not form if the system starts with a fixed angular velocity and subsequently the temperature is lowered down to the A$_2$ phase. It is estimated that the external magnetic field with strength on the order of 1 T is required to have a sufficiently large domain in the temperature-magnetic field phase diagram to have a stable HQV.Comment: 5 pages, 5 figure