The tunable parameter on the object average degree .

<p>The black, red, green, blue and dark yellow lines are for the recommendation list lengths of , 20, 30, 40 and 50, respectively.</p

The inter-diversity on the recommendation list length .

<p>The black, red, green and blue lines are for the HHP, PBS, OHHP and SCL methods, respectively.</p

Symmetric Post-Transition State Bifurcation Reactions with Berry Pseudomagnetic Fields

We investigate how the Berry force (i.e., the pseudomagnetic force operating on nuclei as induced by electronic degeneracy and spin–orbit coupling (SOC)) might modify a post-transition state bifurcation (PTSB) reaction path and affect product selectivity for situations when multiple products share the same transition state. To estimate the magnitude of this effect, Langevin dynamics are performed on a model system with a valley-ridge inflection (VRI) point in the presence of a magnetic field (that mimics the Berry curvature). We also develop an analytic model for such selectivity that depends on key parameters such as the surface topology, the magnitude of the Berry force, and the nuclear friction. Within this dynamical model, static electronic structure calculations (at the level of generalized Hartree–Fock with spin–orbit coupling (GHF+SOC) theory) suggest that electronic spin induced Berry force effects may indeed lead to noticeable changes in methoxy radical isomerization

The tunable parameter on the object degree .

<p>The black and red lines are for the SCL and OHHP methods, respectively.</p

The performance of the PBS, HHP, OHHP and SCL methods.

<p>The overall ranking score , the object-degree dependent ranking score , the overall precision , the object-degree dependent precision , the overall recall , the object-degree dependent recall , the novelty , the inter-diversity and the inner-diversity of the PBS, HHP, OHHP and SCL methods are shown for the <i>Netflix</i>(<i>NET</i>), the <i>MovieLens</i>(<i>MOV</i>) and the <i>RYM</i>, with .</p

An illustration of the resource reallocation process.

<p>(a) for the PBS method, and (b) for the HTS method.</p

The inner-diversity on the recommendation list length .

<p>The black, red, green and blue lines are for the HHP, PBS, OHHP and SCL methods, respectively.</p

The improvement percentage of the SCL against the PBS, HHP and OHHP methods.

<p>The improvement percentage of the SCL against the PBS, HHP and OHHP in the overall ranking score , the object-degree dependent ranking score , the overall precision , the object-degree dependent precision , the overall recall , the object-degree dependent recall , the novelty , the inter-diversity and the inner-diversity are shown for the <i>Netflix</i>(<i>NET</i>), the <i>MovieLens</i>(<i>MOV</i>) and the <i>RYM</i>, with . To guide the eyes, if the indicator of the SCL outperforms other methods, we show the improvement percentage as a positive value, otherwise, as a negative value. The blank in the form indicates an infinite value owing to the zero value of the PBS’s precision and recall.</p

The rescaled tunable parameter vs. the rescaled object average degree .

<p>The black, red, green, blue and dark yellow lines are for the recommendation list lengths of , 20, 30, 40 and 50, respectively.</p

The novelty on the recommendation list length .

<p>The black, red, green and blue lines are for the HHP, PBS, OHHP and SCL methods, respectively.</p