On covering problems of codes

LetC be a binary code of lengthn (i.e., a subset of {0, 1} ⁿ ). TheCovering Radius of C is the smallest integerr such that each vector in {0, 1} ⁿ is at a distance at mostr from some code word. Our main result is that the decision problem associated with the Covering Radius of arbitrary binary codes is NP-complete. This result is established as follows. TheRadius of a binary codeC is the smallest integerr such thatC is contained in a radius-r ball of the Hamming metric space 〈{0, 1} ⁿ ,d〉. It is known [K] that the problems of computing the Radius and the Covering Radius are equivalent. We show that the 3SAT problem is polynomially reducible to the Radius decision problem. A central tool in our reduction is a metrical characterization of the set ofdoubled vectors of length 2n: {v=(v ₁ v ₂ …v _2n ) | ∀i:v _2i =v _2i−1}. We show that there is a setY ⊂ {0, 1}²ⁿ such that for everyv ε {0, 1}²ⁿ :v is doubled iffY is contained in the radius-n ball centered atv; moreover,Y can be constructed in time polynomial inn.     

Two-step compensation of nonlinear systems

We study the problem of stabilization of nonlinear plants. We show that given a nonlinear plant P, if there exists a (nonlinear) compensator F, possibly unstable, which stabilizes P, then, with P₁: = P(I − F(− P))⁻¹, any C defined by C:= F + Q(I − P₁Q)⁻¹ for some finite-gain stable Q will stabilize P.     

Relation between power and endurance for treadmill running of short duration

Abstract

An exercise test was devised to investigate the relationship between power and endurance for treadmill running. The subjects were 19 males aged 21-25 yr (11 distance runners and 4 sprinters of provincial grade, and 4 non-competitive runners). Each subject ran to exhaustion on a treadmill at 15kmhr^?1at five different inclinations (31%-9%), giving maximum performance times in the range 10s to 3 min. An iterative least-squares procedure was used to fit the following exponential model to each subject's data: I₁= I_∞+ (I₀?I_∞)exp(?t/τ) where I₁, I₀and 1_∞are inclinations at time t = t, t = 0 and t → ∞, and τ is a time constant. The fit was excellent (r ²= 0.96? 1.00). I₀and 1_∞are interpreted as measures of maximum anaerobic (instantaneous) and maximum aerobic (continuous) power respectively. Inclinations corresponding to performance times of 10-180s (I₁₀?I₁₈₀) were calculated from these parameters. Test-retest reliability was highest for I₀-I₃₀(intraclass r= 0.97?0.94), lower for I₆₀-I_∞(r= 0.89?0.84), and lowest for τ (r= 0.78). Good correlations were observed between I₀-I₃₀and peak power in a 30s all-out test on a cycle ergometer (r= 0.73?0.81), and between I₁₈₀, I_∞and maximum oxygen consumption (r= 0.87, 0.81). The test may be useful for ranking or monitoring running performance for events of up to 1 min duration.     

Aerodynamic drag in field cycling with special reference to the Obree's position

In cycling at race speeds, 90% of total resistance opposing motion, R _T(N) T depends on aerodynamic drag of air, which is directly proportional to the effective frontal area, AC _d(m²). R _T was measured on a cyclist, in an open velodrome, in order to evaluate AC _d in four different positions on a traditional bicycle: upright d position (UP), dropped position (DP), aero position (AP) and Obree's position (OP : the hands in support under the chest, the forearms tucked on the arms, the trunk tilted forward). R _T was determined at different constant speeds, Vc(m s^?1) with a special device (Max One), which allows the measurement of the external mechanical power P _ext(W) in real conditions of cycling locomotion ext (R _T = P _ext Vc^?1). Experiments were carried out in order to test the validity and the reproducibility of P _ext provided by the measurement device. P _ext was measured twice in the same experimental conditions (exercise on a treadmill against slopes varying from 1 to 14%) and no significant difference was observed between the two measurement series. A systematic measurement error was observed allowing the use of a correcting factor. As expected, in the four rider positions, R _T increased linearly (p<0.001, r = 0.90-0.95) with Vc². AC _d were significantly different (p<0.001) between the four positions, except between DP and AP. As compared to UP, in DP, AP and OP the significant reductions of AC _d were 7.8, 12.4 and 27.8%, respectively. These reductions were associated with the degree of rachis flexion and with the decrease of the lateral distance between the two upper limbs. In UP, AC _d (0.299 m²) was lower (-23%) than those reported in previous studies. In DP and AP, AC _d (0.276 m² and 0.262 m², respectively) were similar to those reported in previous studies. In OP, no study allowed a real comparison with the value of AC _d (0.216 m²) found in this study. The average rolling resistance (Rr = 1.95±0.81 N) determined according to the four positions was in line with previous reports. These findings suggest that the position adopted by Obree significantly reduces the aerodynamic drag and, thus, is an important factor in cycling performance.     

The super laceability of the hypercubes

A k-containerC(u,v) of a graph G is a set of k disjoint paths joining u to v. A k-container C(u,v) is a k∗-container if every vertex of G is incident with a path in C(u,v). A bipartite graph G is k∗-laceable if there exists a k∗-container between any two vertices u, v from different partite set of G. A bipartite graph G with connectivity k is super laceable if it is i∗-laceable for all i?k. A bipartite graph G with connectivity k is f-edge fault-tolerant super laceable if G−F is i∗-laceable for any 1?i?k−f and for any edge subset F with |F|=f<k−1. In this paper, we prove that the hypercube graph Q_r is super laceable. Moreover, Q_r is f-edge fault-tolerant super laceable for any f?r−2.     

Quantitative prediction of overall seat discomfort

Static seat characteristics (seat stiffness) and dynamic seat characteristics (vibration magnitude) can both influence judgements of seat comfort. It is proposed that seat comfort can be predicted on the basis of Steven's psychophysical law: ψ = k?n , where ψ is a sensation magnitude, ? is the stimulus magnitude and k is a constant. The law is modified to: ψ = a + b?ns s + c?nv v, where ? s ? v represent seat stiffness and vibration magnitude, n s and n v are exponents determined by the rate of increase in discomfort associated with the stiffness and vibration magnitude, and a, b and c are constants. The stiffness of foam loaded to 490 N may indicate static seat comfort, while the vibration dose value (VDV) on the seat surface may indicate vibration discomfort. Two experiments with 20 subjects investigated this approach. The first experiment with five magnitudes of vibration, three foams and a rigid wooden flat seat yielded 0.929 for the exponent, n v, for VDV. In the second experiment subjects judged the overall seat discomfort while exposed six vibration magnitudes with the same four seating conditions. This experiment yielded 1.18 for the exponent, n s, for seat stiffness. The overall prediction of seat discomfort was given by: ψ = -50.3+ 2.68 ? s 1.18+ 101 ? v 0.929. The prediction equation provided more accurate estimates of subject discomfort than models using either the VDV alone or the stiffness alone, especially when the vibration magnitude was low or the seats were similar. An interaction variable between the VDV and the stiffness slightly improved the prediction. The equivalence of the two stimuli was given by log10 (stiffness) = 0.787 log10 (VDV)+ 1.34, or log10 (VDV) = 1.27 log10 (stiffness)? 1.70.     

DEPARTMENT OF SCIENTIFIC AND INDUSTRIAL RESEARCH: HUMAN SCIENCES COMMITTEE

Maximal power output during short term constant velocity cycling and vertical jumping from a force platform has been studied in five healthy young male subjects. From the measurements on the force platform the peak (instantaneous) power output (P), net impulse (I_N ), force (F₁ ). velocity of take-off(V_T ) and height of jump(h) were calculated. The corresponding values for power (H), force (F) and velocity (V) on the bicycle were obtained from analysis of the force-velocity relationship.

The results (mean ± S.D.) showed that on the force platform F₁ P, I_N, V_T and h were 1073± 167N, 2205±310W, 154±17Ns, 2·48+0·15ms^?1 and 31 +4cm. h was positively associated with both I_N (r= +0·77) and P (r = 0·67). The mean maximal power output for cycling was 854W(39%) greater than jumping and was achieved at a 271N (25%) increase in F and a reduction in V. Nevertheless they were closely related.

Platform P(W) = 717·6 + 0·483 bicycle H(W) r= +0·74

A comparison of linear and curvilinear (hyperbolic) analysis of the F/V bicycle data showed that the latter did not reduce the variance of observations and was not, therefore, statistically justifiable (Wilkie 1950). The mean intra-subject variations of P and H were 6·6%± 1·8 and 40%+1·2. The relative values of F and V at H were both found to be approximately 50% of their respective maximal values.

It was concluded that short term power output can be measured simply and accurately in man during the performance of two activities. Rotational movement of the legs as in cycling produces higher values of peak power output then vertically lifting body weight. For the achievement of peak power output in cycling, relative force and speed of movement must both correspond to approximately half of their respective maximal values.     

Time-series decomposition and forecasting

Any stationary time-series can be decomposed by means of an optimization operator, called the ζ-optimator, into several components (the time-series){Y _t ⁱ}, i =1,2,…, p, such that the first component {V _t ⁱ} t = 1,2,…,v is a smooth process having a larger autocorrelation in comparison with the original process {Y _t}, i.e. ρ_vi > ρ_y. Usually only a few such components are sufficient for approximating the time-series with good accuracy. The ζ-optimator involves a shape parameter a, so the decomposition is unique provided that a. is fixed. Since the component {V _t ¹} involves much of the useful information it can be used for computing predictors for control purposes. Thus, given the observations Y_v, Y_v-1, Y_v-2,…, a predictor of Y_v+1 is ρ_vi V _v ¹ (q) where, V_v ¹(q) = qY^v + q(1-q)² Y_v-2, …, the weights q(1-q)^r, r=0,1,2,…, decreasing rapidly as q = q(α) ε (0,1) Further, one may choose q rather than choosing α, since q(α) is a one-one mapping. Once q is fixed, the predictor ρ_v1 V _v ¹(q) is obtained in a straightforward way by using the formula above. It is shown that ρ_v1 V _v ¹(q) converges to the best predictor as α → 0. Some examples are worked out, illustrating both the decomposition and the forecasting procedures.     

The Intersection of Two Ringed Surfaces and Some Related Problems

We present an efficient and robust algorithm to compute the intersection curve of two ringed surfaces, each being the sweep ∪_uC^u generated by a moving circle. Given two ringed surfaces ∪_uC^u₁ and ∪_vC^v₂, we formulate the condition C^u₁ ∩ C^v₂ ≠ ∅ (i.e., that the intersection of the two circles C^u₁ and C^v₂ is nonempty) as a bivariate equation λ(u, v)=0 of relatively low degree. Except for redundant solutions and degenerate cases, there is a rational map from each solution of λ(u, v)=0 to the intersection point C^u₁ ∩ C^v₂. Thus it is trivial to construct the intersection curve once we have computed the zero-set of λ(u, v)=0. We also analyze exceptional cases and consider how to construct the corresponding intersection curves. A similar approach produces an efficient algorithm for the intersection of a ringed surface and a ruled surface, which can play an important role in accelerating the ray-tracing of ringed surfaces. Surfaces of linear extrusion and surfaces of revolution reduce their respective intersection algorithms to simpler forms than those for ringed surfaces and ruled surfaces. In particular, the bivariate equation λ(u, v)=0 is reduced to a decomposable form, f(u)=g(v) or 6f(u)−g(v)6=|r(u)|, which can be solved more efficiently than the general case.     

Actions,finite state sets and applications to trees

Let M be a monoid acting on a set X; for any x?X and A?X we put x ^?1 A = {m?M/xm?A}. Call A?X finite state if card {x ^?1 A/x?X} <∞.

The finite state subsets of T _Σvia the action T _Σ × P _Σ→T _Σare the recognizable forests (P _Σis the monoid of all Σ-trees with just one leaf labeled by a variable x).

Next we prove that the recognizability of forests is equivalent to the finiteness of a certain “syntactic” monoid A Mezei's-like theorem for trees is established: the finite state subsets of T _Σ × T_г are exactly the finite unions of sets of sets of the form B × C B?Rec(T _Σ) and C?Rec(T _г) Another characterization of such relations is given using bimorphisms.     

Right,left characteristic sequences and column,row minimal indices of a singular pencil

For a general singular pencil sF — G?? ^m×n [s] the right, left characteristic sequences _r(F, G), _l(F, G) are defined and they are shown to be of the piecewise arithmetic progression type. The sets of column, row minimal indices ?_c(F, G), ?_r(F, G) are defined by a singular points analysis of _r(F, G), ?_l(F, G) respectively. Thus, ?_c(F, G), ?_r(F, G) emerge as numerical invariants of the ordered pair (F, G) and they may be computed by rank tests on Toeplitz matrices defined on (F, G).     

Sun-stimulated chlorophyll fluorescence 2: Impact of atmospheric properties

Abstract

The Sun-stimulated chlorophyll fluorescence is a small but significant property of phytoplankton which can be detected using remote-sensing techniques. Besides the influence of oceanic properties, chlorophyll fluorescence is masked by atmospheric extinction. While an increase in chlorophyll concentration of 1 mg/m³ causes an increase in the upwelling radiances of about 0·03Wm^?2sr^?1 μm^?1 just above the water surface and due to the chlorophyll fluorescence, the upward radiances measured at λ_F = 685nm and at the top of the atmosphere ranges from 8 to 20Wm^?2sr^?1 μm^?1 for realistic atmospheric turbidity variations and a solar zenith distance of Θ_s = 50·7°. Additionally, the fluorescence, peaking at λ_F = 685nm with a half-width of about 10 nm, is reduced by the absorption of O₂ and H₂O. However, the fluorescence signal is nearly unaffected, when wavelengths λ≥686nm are exluded and a spectral interval of Δλ_F = 5nm is used for the radiance measurements.     

The relation between cycling time to exhaustion and anaerobic threshold

Abstract

This study investigated whether the anaerobic threshold (AnT) could be used to predict prolonged work capacity measured as cycling time to exhaustion (= endurance time) and which factors, in addition to relative exercise intensity, could explain variation in endurance time. Theoretical exercise intensities corresponding to certain endurance times were also calculated. The hyperbolic and exponential functions between cycling time and relative work rate (WR[%]), as well as between cyling time and relative oxygen uptake ([Vdot]O₂[%]) were fitted to the pooled data (n = 45) of 17 subjects. The WR(%) and [Vdot]O₂ (%) were expressed as a percentage of the subject's own AnT- and maximum -values. At WR corresponding to AnT (i.e., 70% of WR_max) an average subject could cycle 60 min according to both AnT- or maximum-related exponential function. When prediction was done for an endurance time of 4 h, the AnT-related exponential function gave 2·9%-units ( = 11 W or ～0·15 O₂1 · min^?1) lower intensity level (51% of WR_max than the maximum-related function (54% of WR_max). The WR(%) alone explained 54% and 70% of the variation in endurance time of the AnT-related and maximum-related exponential functions, respectively. Muscle fibre composition and initial blood lactate or relative muscle glycogen depletion (change in muscle glycogen as percentage) increased significantly the explanatory power of these models. The differences between the observed and expected exercise times correlated with blood lactate accumulation (r = ?0·42; p < 0·01), muscle fibre composition (r = 0·33; p < 0·05) and relative muscle glycogen depletion (r = 0·67; p < 0·01). It was concluded that the capacity for prolonged work measured as cycling time to exhaustion can be estimated by AnT-related power output, and that the exponential function model is the most suitable. Prediction power of the model can be improved by multiple regressions including muscle fibre composition, initial blood lactate level and relative muscle glycogen depletion.     

The ergonomics of different tyres and tyre pressure during wheelchair propulsion

It is believed that the newer solid tyres on wheelchairs perform as well as pneumatic tyres along with less cost and time for maintenance. The questions are: (1) do solid tyres perform as well as pneumatic tyres and (2) what is the critical level of pneumatic tyre pressure before wheeling efficiency decreases? Part one measured the rolling resistance differences of five commonly used wheelchair tyres (three pneumatic and two solid) under four different tyre pressures (100, 75, 50 and 25 of inflation). Part two measured the oxygen consumption in 15 participants with paraplegia, during wheelchair propulsion, comparing the same four levels of tyre inflation. The solid tyres performed worse than all three pneumatic tyres even when tyres were under-inflated to 25% of tyre pressure. Two of the pneumatic tyres showed significant decreases in rolling between 100 and 50%, but there were no significant differences in rolling distance between 100 and 75% pressure. The physiological study showed that energy expenditure increased significantly at 50% of tyre-inflation. Health care facilities are finding ways to decrease cost by using solid tyres on all wheelchairs. This study shows that benefits to clients and staff using pneumatic tyres far outweigh the minimal cost in time to maintain adequate tyre inflation.     

Simultaneously controllable fuzzy matrices

Let F be a set of n × n fuzzy matrices. F is called simultaneously controllable if there exists a permutation matrix P such that for each A ε F, C = [c_ij] = P A P^T satisfies c_ij ≥ c_ji for i > j, where is the max-min composition. In this paper, the necessary and sufficient conditions for a set of n × n fuzzy matrices to be simultaneously controllable will be established. A constructive algorithm which can determine a simultaneously controllable set of n × n fuzzy matrices is presented as well.     

A Simple Optimal Parallel Algorithm for a Core of a Tree

A core of a tree T = (V, E) is a path in T which minimizes ∑_vVd(v, P), where d(v, P), the distance from a vertex v to path P, is defined as min_uPd(v, u). We present an optimal parallel algorithm to find a core of T in O(log n) time using O(n/log n) processors on an EREW PRAM machine, where n is the number of vertices of tree T.     

Characterizing r-perfect codes in direct products of two and three cycles

An r-perfect code of a graph G=(V,E) is a set C⊆V such that the r-balls centered at vertices of C form a partition of V. It is proved that the direct product of Cm and Cn (r?1, m,n?2r+1) contains an r-perfect code if and only if m and n are each a multiple of ²(r+1)+r² and that the direct product of Cm, Cn, and C? (r?1, m,n,??2r+1) contains an r-perfect code if and only if m, n, and ? are each a multiple of r³+³(r+1). The corresponding r-codes are essentially unique. Also, r-perfect codes in C2r×Cn (r?2, n?2r) are characterized.     

Insider and outsider person authentication with minimum number of brain wave signals by neural and homogeneous identity filtering

This study discusses the uniqueness of brain wave signals (electroencephalography, EEG) in a singular individual to determine personal authentication. The brain is the most complex biological structure known to man and its wave signals are very difficult to mimic or steal, EEG signals can be measured from different locations, but too many signals can degrade recognition speed and accuracy. A practical technique combining independent component analysis for signal cleaning and a supervised neural network for authenticating signals was proposed. This new process called homogeneous identify filtering was introduced to identify persons in considered and outside groups. From 16 different EEG signal locations, four truly relevant locations of 1,000 data points (F ₄, C ₄, P ₄, O ₂), 1,500 data points (F ₈, F ₃, C ₃, P ₄), and 3,000 data points (F _p1, F ₄, P ₄, O ₂) by SOBIRO algorithm were selected. This selection was used to identify 20 persons with high accuracy within the test group. The significant location for authentication is position P ₄ which is the parietal lobe of the brain.

     

Bio‐optical properties and estimation of the optically active substances in Lake Tianmuhu in summer

Bio‐optical properties in an optically complex and biologically productive region of Lake Tianmuhu were determined in three cruises from June to August 2006. The concentrations of three optically active substances, tripton C _Tripton (calculated from total suspended matter and chlorophyll‐a (Chla) and phaeophytin‐a (Pa)), phytoplankton pigment C _Chla+Pa , and chromophoric dissolved organic matter (CDOM) a _CDOM(440), were predicted from the estimated irradiance reflectance based on in situ measurements and laboratory analyses. The total relative contributions of phytoplankton, tripton, CDOM and pure water over the range of photosynthetically active radiation (PAR) (400–700 nm) were 36.1%, 24.2%, 15.9% and 23.8%, respectively. The dominant contribution of phytoplankton to the total absorption was due to high phytoplankton pigment concentration. The range and variation in irradiance reflectance and diffuse attenuation coefficient derived from a bio‐optical model, based on inherent optical properties, compared well with the measured variability. A reasonably strong relationship (R² = 0.92) was observed between irradiance reflectance at 780 nm R(780) and C _Tripton. For our data set, the best algorithm for C _Chla+Pa used the three‐band reflectance model [R ^?1(688)?R ^?1(717)]×R(747). The a _CDOM(440) could be estimated using the ratio of irradiance reflectance R(682)/R(555). The retrieval accuracy (R²) of tripton, phytoplankton pigment and CDOM was 0.92, 0.87 and 0.91, respectively, while the rms. error was 0.90 mg l^?1 (18.2%), 3.27 µg l^?1 (14.8%) and 0.073 m^?1 (15.3%), respectively. Estimation of the concentrations of the three optically active substances was reasonably accurate based on inherent optical properties measurement.     

The ergonomics of different tyres and tyre pressure during wheelchair propulsion

It is believed that the newer solid tyres on wheelchairs perform as well as pneumatic tyres along with less cost and time for maintenance. The questions are: (1) do solid tyres perform as well as pneumatic tyres and (2) what is the critical level of pneumatic tyre pressure before wheeling efficiency decreases? Part one measured the rolling resistance differences of five commonly used wheelchair tyres (three pneumatic and two solid) under four different tyre pressures (100, 75, 50 and 25 of inflation). Part two measured the oxygen consumption in 15 participants with paraplegia, during wheelchair propulsion, comparing the same four levels of tyre inflation. The solid tyres performed worse than all three pneumatic tyres even when tyres were under-inflated to 25% of tyre pressure. Two of the pneumatic tyres showed significant decreases in rolling between 100 and 50%, but there were no significant differences in rolling distance between 100 and 75% pressure. The physiological study showed that energy expenditure increased significantly at 50% of tyre-inflation. Health care facilities are finding ways to decrease cost by using solid tyres on all wheelchairs. This study shows that benefits to clients and staff using pneumatic tyres far outweigh the minimal cost in time to maintain adequate tyre inflation.